Georgian Mathematical Journal最新文献

{"title":"Finite groups in which some particular invariant subgroups are TI-subgroups or subnormal subgroups","authors":"Yifan Liu, Jiangtao Shi","doi":"10.1515/gmj-2024-2001","DOIUrl":"https://doi.org/10.1515/gmj-2024-2001","url":null,"abstract":"Let <jats:italic>A</jats:italic> and <jats:italic>G</jats:italic> be finite groups such that <jats:italic>A</jats:italic> acts coprimely on <jats:italic>G</jats:italic> by automorphisms. We prove that if every self-centralizing non-nilpotent <jats:italic>A</jats:italic>-invariant subgroup of <jats:italic>G</jats:italic> is a TI-subgroup or a subnormal subgroup, then every non-nilpotent <jats:italic>A</jats:italic>-invariant subgroup of <jats:italic>G</jats:italic> is subnormal and <jats:italic>G</jats:italic> is <jats:italic>p</jats:italic>-nilpotent or <jats:italic>p</jats:italic>-closed for any prime divisor <jats:italic>p</jats:italic> of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">|</m:mo> <m:mi>G</m:mi> <m:mo stretchy=\"false\">|</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2001_eq_0039.png\" /> <jats:tex-math>{|G|}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. If every self-centralizing non-metacyclic <jats:italic>A</jats:italic>-invariant subgroup of <jats:italic>G</jats:italic> is a TI-subgroup or a subnormal subgroup, then every non-metacyclic <jats:italic>A</jats:italic>-invariant subgroup of <jats:italic>G</jats:italic> is subnormal and <jats:italic>G</jats:italic> is solvable.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139590014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized essential spectra involving the class of g-g-Riesz operators","authors":"Imen Ferjani, Omaima Kchaou, Bilel Krichen","doi":"10.1515/gmj-2024-2002","DOIUrl":"https://doi.org/10.1515/gmj-2024-2002","url":null,"abstract":"In this paper, we explore the spectral properties of unbounded generalized Fredholm operators acting on a non-reflexive Banach space <jats:italic>X</jats:italic>. The results are formulated in terms of some topological conditions made on <jats:italic>X</jats:italic> or on its dual <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>X</m:mi> <m:mo>*</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2002_eq_0247.png\" /> <jats:tex-math>{X^{*}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In addition, we introduce the concept of the so-called g-g-Riesz linear operators as an extension of Riesz operators. The obtained results are used to discuss the incidence of the behavior of generalized essential spectra. Furthermore, a relation between the generalized essential spectrum and the left (resp. the right) essential spectrum by means of g-Riesz perturbation is provided.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition","authors":"Abdeljalil Nachaoui, Tea Shavadze, Tamaz Tadumadze","doi":"10.1515/gmj-2023-2122","DOIUrl":"https://doi.org/10.1515/gmj-2023-2122","url":null,"abstract":"The analytic relation between solutions of the original Cauchy problem and a corresponding perturbed problem is established. In the representation formula of solution, the effects of the discontinuous initial condition and perturbation of the initial data are revealed.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on b-generalized (α,β)-derivations in prime rings","authors":"Nripendu Bera, Basudeb Dhara","doi":"10.1515/gmj-2023-2121","DOIUrl":"https://doi.org/10.1515/gmj-2023-2121","url":null,"abstract":"Let <jats:italic>R</jats:italic> be a prime ring, let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>0</m:mn> <m:mo>≠</m:mo> <m:mi>b</m:mi> <m:mo>∈</m:mo> <m:mi>R</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2121_eq_0112.png\" /> <jats:tex-math>{0neq bin R}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and let α and β be two automorphisms of <jats:italic>R</jats:italic>. Suppose that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>F</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mi>R</m:mi> <m:mo>→</m:mo> <m:mi>R</m:mi> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2121_eq_0147.png\" /> <jats:tex-math>{F:Rrightarrow R}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mi>F</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>:</m:mo> <m:mrow> <m:mi>R</m:mi> <m:mo>→</m:mo> <m:mi>R</m:mi> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2121_eq_0155.png\" /> <jats:tex-math>{F_{1}:Rrightarrow R}</jats:tex-math> </jats:alternatives> </jats:inline-formula> are two <jats:italic>b</jats:italic>-generalized <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>β</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2121_eq_0103.png\" /> <jats:tex-math>{(alpha,beta)}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-derivations of <jats:italic>R</jats:italic> associated with the same <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>β</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2121_eq_0103.png\" /> <jats:tex-math>{(alpha,beta)}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-derivation <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>d</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mi>R</m:mi> <m:mo>→</m:mo> <m:mi>R</m:mi> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2121_eq_0098.png\" /> <jats:tex-math>d:Rrightarrow R</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>G</m:mi>","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139103439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical approaches for solution of hyperbolic difference equations on circle","authors":"Allaberen Ashyralyev, Fatih Hezenci, Yasar Sozen","doi":"10.1515/gmj-2023-2103","DOIUrl":"https://doi.org/10.1515/gmj-2023-2103","url":null,"abstract":"The present paper considers nonlocal boundary value problems for hyperbolic equations on the circle <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi mathvariant=\"double-struck\">T</m:mi> <m:mn>1</m:mn> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2103_ineq_0001.png\" /> <jats:tex-math>mathbb{T}^{1}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The first-order modified difference scheme for the numerical solution of nonlocal boundary value problems for hyperbolic equations on a circle is presented. The stability and coercivity estimates in various Hölder norms for solutions of the difference schemes are established. Moreover, numerical examples are provided.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiplicity result for a (p(x),q(x))-Laplacian-like system with indefinite weights","authors":"Khaled Kefi, Chaima Nefzi","doi":"10.1515/gmj-2023-2107","DOIUrl":"https://doi.org/10.1515/gmj-2023-2107","url":null,"abstract":"Under some suitable conditions, we show that at least three weak solutions exist for a system of differential equations involving the <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:mi>q</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2107_eq_0108.png\" /> <jats:tex-math>{(p(x),q(x))}</jats:tex-math> </jats:alternatives> </jats:inline-formula> Laplacian-like with indefinite weights. The proof is related to the Bonanno–Marano critical theorem (<jats:italic>Appl. Anal.</jats:italic> 89 (2010), 1–10).","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two presentations of a weak type inequality for geometric maximal operators","authors":"Paul Hagelstein, Giorgi Oniani, Alex Stokolos","doi":"10.1515/gmj-2023-2113","DOIUrl":"https://doi.org/10.1515/gmj-2023-2113","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi mathvariant=\"normal\">Φ</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi mathvariant=\"normal\">∞</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>→</m:mo> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi mathvariant=\"normal\">∞</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2113_eq_0076.png\" /> <jats:tex-math>{Phi:[0,infty)rightarrow[0,infty)}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a Young’s function satisfying the <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"normal\">Δ</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2113_eq_0070.png\" /> <jats:tex-math>{Delta_{2}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-condition and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>M</m:mi> <m:mi mathvariant=\"script\">ℬ</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2113_eq_0063.png\" /> <jats:tex-math>{M_{mathcal{B}}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be the geometric maximal operator associated to a homothecy invariant basis <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℬ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2113_eq_0098.png\" /> <jats:tex-math>{mathcal{B}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> acting on measurable functions on <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2113_eq_0090.png\" /> <jats:tex-math>{mathbb{R}^{n}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Let <jats:italic>Q</jats:italic> be the unit cube in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2113_eq_0090.png\" /> <jats:tex-math>{mathbb{R}^{n}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mi>L</m:mi> <m:mi mathvariant=\"normal\">Φ</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Centralizing identities involving generalized derivations in prime rings","authors":"Vincenzo De Filippis, Pallavee Gupta, Shailesh Kumar Tiwari, Balchand Prajapati","doi":"10.1515/gmj-2023-2109","DOIUrl":"https://doi.org/10.1515/gmj-2023-2109","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2109_eq_0519.png\" /> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a prime ring of characteristic not equal to 2, let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">𝒰</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2109_eq_0527.png\" /> <jats:tex-math>{mathcal{U}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be Utumi quotient ring of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2109_eq_0519.png\" /> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">𝒞</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2109_eq_0481.png\" /> <jats:tex-math>{mathcal{C}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be the extended centroid of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2109_eq_0519.png\" /> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Let Δ be a generalized derivation on <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2109_eq_0519.png\" /> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>δ</m:mi> <m:mn>1</m:mn> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2109_eq_0428.png\" /> <jats:tex-math>{delta_{1}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>δ</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2109_eq_0440.png\" /> <jats:tex-math>{delta_{2}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be derivations on <jats:inline-form","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost measurable functions on probability spaces","authors":"Alexander Kharazishvili","doi":"10.1515/gmj-2023-2120","DOIUrl":"https://doi.org/10.1515/gmj-2023-2120","url":null,"abstract":"The notion of (real-valued) almost measurable functions on probability spaces is introduced and some of their properties are considered. It is shown that any almost measurable function may be treated as a quasi-random variable in the sense of [A. Kharazishvili, On some version of random variables, Trans. A. Razmadze Math. Inst. 177 2023, 1, 143–146].","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On φ-u-S-flat modules and nonnil-u-S-injective modules","authors":"Hwankoo Kim, Najib Mahdou, El Houssaine Oubouhou","doi":"10.1515/gmj-2023-2117","DOIUrl":"https://doi.org/10.1515/gmj-2023-2117","url":null,"abstract":"This paper introduces and studies the ϕ-u-<jats:italic>S</jats:italic>-flat (resp., nonnil-u-<jats:italic>S</jats:italic>-injective) modules, which are a generalization of both ϕ-flat modules and u-<jats:italic>S</jats:italic>-flat modules (resp., both nonnil-injective modules and u-<jats:italic>S</jats:italic>-injective modules). We give the Cartan–Eilenberg–Bass theorem for nonnil-u-<jats:italic>S</jats:italic>-Noetherian rings. Finally, we offer some new characterizations of the ϕ-von Neumann regular ring.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}