Journal of Algebra and Its Applications最新文献

{"title":"Finite dimensional Frobenius-Perron Algebras","authors":"Yongjun Xu, Yikun Liu","doi":"10.1142/s0219498825502640","DOIUrl":"https://doi.org/10.1142/s0219498825502640","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140745030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"2-Local derivations of Heisenberg-Virasoro type Lie algebras","authors":"Chunguang Xia, Xiao Dong, Tianyu Ma","doi":"10.1142/s0219498825502615","DOIUrl":"https://doi.org/10.1142/s0219498825502615","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140741631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Divisor Graphs and Symmetries of Finite Abelian Groups","authors":"John D. LaGrange","doi":"10.1142/s0219498825502664","DOIUrl":"https://doi.org/10.1142/s0219498825502664","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140743009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local and 2-local derivations on filiform associative algebras","authors":"Kobiljon Abdurasulov, Shavkat Ayupov, Bakhtiyor Yusupov","doi":"10.1142/s0219498825502421","DOIUrl":"https://doi.org/10.1142/s0219498825502421","url":null,"abstract":"<p>This paper is devoted to the study of local and 2-local derivations of null-filiform, filiform and naturally graded quasi-filiform associative algebras. We prove that these algebras as a rule admit local derivations which are not derivations. We show that filiform and naturally graded quasi-filiform associative algebras admit 2-local derivations which are not derivations and any 2-local derivation of null-filiform associative algebras is a derivation.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study of a division-like property","authors":"Robin Khanfir, Béranger Seguin","doi":"10.1142/s0219498825502214","DOIUrl":"https://doi.org/10.1142/s0219498825502214","url":null,"abstract":"<p>We study a weak divisibility property for noncommutative rings: A nontrivial ring is <i>fadelian</i> if for all nonzero <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>a</mi></math></span><span></span> and <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>x</mi></math></span><span></span> there exist <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>b</mi><mo>,</mo><mi>c</mi></math></span><span></span> such that <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>x</mi><mo>=</mo><mi>a</mi><mi>b</mi><mo stretchy=\"false\">+</mo><mi>c</mi><mi>a</mi></math></span><span></span>. We prove properties of fadelian rings and construct examples thereof which are not division rings, as well as non-Noetherian and non-Ore examples.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Haar measure of a profinite n-ary group","authors":"M. Shahryari, M. Rostami","doi":"10.1142/s0219498825502196","DOIUrl":"https://doi.org/10.1142/s0219498825502196","url":null,"abstract":"<p>We prove that every profinite <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span>-ary group <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>G</mi><mo>,</mo><mi>f</mi><mo stretchy=\"false\">)</mo><mo>=</mo><msub><mrow><mstyle><mtext mathvariant=\"normal\">der</mtext></mstyle></mrow><mrow><mi>𝜃</mi><mo>,</mo><mi>b</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>G</mi><mo>,</mo><mo stretchy=\"false\">•</mo><mo stretchy=\"false\">)</mo></math></span><span></span> has a unique Haar measure <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>m</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span><span></span> and further for every measurable subset <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>A</mi><mo>⊆</mo><mi>G</mi></math></span><span></span>, we have <disp-formula-group><span><math altimg=\"eq-00007.gif\" display=\"block\" overflow=\"scroll\"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>p</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>A</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mi>m</mi><mo stretchy=\"false\">(</mo><mi>A</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mo stretchy=\"false\">(</mo><mi>n</mi><mo stretchy=\"false\">−</mo><mn>1</mn><mo stretchy=\"false\">)</mo><msup><mrow><mi>m</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup><mo stretchy=\"false\">(</mo><mi>A</mi><mo stretchy=\"false\">)</mo><mo>,</mo></mrow></math></span><span></span></disp-formula-group> where <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi></math></span><span></span> and <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>m</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup></math></span><span></span> are the normalized Haar measures of the profinite groups <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>G</mi><mo>,</mo><mo stretchy=\"false\">•</mo><mo stretchy=\"false\">)</mo></math></span><span></span> and the Post cover <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>G</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup></math></span><span></span>, respectively.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On (naturally) semifull and (semi)separable semifunctors","authors":"Lucrezia Bottegoni","doi":"10.1142/s0219498825502111","DOIUrl":"https://doi.org/10.1142/s0219498825502111","url":null,"abstract":"<p>The notion of semifunctor between categories, due to [9], is defined as a functor that does not necessarily preserve identities. In this paper, we study how several properties of functors, such as fullness, full faithfulness, separability, natural fullness, can be formulated for semifunctors. Since a full semifunctor is actually a functor, we are led to introduce a notion of semifullness (and then semifull faithfulness) for semifunctors. In order to show that these conditions can be derived from requirements on the hom-set components associated with a semifunctor, we look at “semisplitting properties” for seminatural tranformations and we investigate the corresponding properties for morphisms whose source or target is the image of a semifunctor. We define the notion of naturally semifull semifunctor and we characterize natural semifullness for semifunctors that are part of a semiadjunction in terms of semisplitting conditions for the unit and counit attached to the semiadjunction. We study the behavior of semifunctors with respect to (semi)separability and we prove Rafael-type Theorems for (semi)separable semifunctors and a Maschke-type theorem for separable semifunctors. We provide examples of semifunctors on which we test the properties considered so far.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cryptanalysis of a key exchange protocol based on a congruence-simple semiring action","authors":"A. Otero Sánchez, J. A. López Ramos","doi":"10.1142/s0219498825502299","DOIUrl":"https://doi.org/10.1142/s0219498825502299","url":null,"abstract":"<p>We show that a previously introduced key exchange based on a congruence-simple semiring action is not secure by providing an attack that reveals the shared key from the distributed public information for any of such semirings.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Images of multilinear polynomials on generalized quaternion algebras","authors":"Peter V. Danchev, Truong Huu Dung, Tran Nam Son","doi":"10.1142/s0219498825502093","DOIUrl":"https://doi.org/10.1142/s0219498825502093","url":null,"abstract":"<p>In connection with the work of Malev published in [<i>J. Algebra Appl.</i><b>13</b> (2014) 1450004; <i>J. Algebra Appl.</i><b>20</b> (2021) 2150074], we continue to provide a classification of possible images of multilinear polynomials on generalized quaternion algebras.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Para-Kähler and pseudo-Kähler structures on Lie–Yamaguti algebras","authors":"Jia Zhao, Yuqin Feng, Yu Qiao","doi":"10.1142/s0219498825502044","DOIUrl":"https://doi.org/10.1142/s0219498825502044","url":null,"abstract":"<p>For a pre-Lie–Yamaguti algebra <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>A</mi></math></span><span></span>, by using its sub-adjacent Lie–Yamaguti algebra <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>A</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span><span></span>, we are able to construct a semidirect product Lie–Yamaguti algebra via a representation of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>A</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span><span></span>. The investigation of such semidirect Lie–Yamaguti algebras leads us to the notions of para-Kähler structures and pseudo-Kähler structures on Lie–Yamaguti algebras, and also gives the definition of complex product structures on Lie–Yamaguti algebras. Furthermore, a Levi–Civita product with respect to a pseudo-Riemannian Lie–Yamaguti algebra is introduced and we explore its relation with pre-Lie–Yamaguti algebras.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}