Journal of Algebra and Its Applications最新文献

{"title":"Morita equivalences on Brauer algebras and BMW algebras of simply-laced types","authors":"Shoumin Liu","doi":"10.1142/s0219498825501749","DOIUrl":"https://doi.org/10.1142/s0219498825501749","url":null,"abstract":"<p>The Morita equivalences of classical Brauer algebras and classical Birman–Murakami–Wenzl (BMW) algebras have been well studied. Here, we study the Morita equivalence problems on these two kinds of algebras of simply-laced type, especially for them with the generic parameters. We show that Brauer algebras and BMW algebras of simply-laced type are Morita equivalent to the direct sums of some group algebras of Coxeter groups and some Hecke algebras of Coxeter groups, respectively.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150602","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":"Certain linear isomorphisms for hyperalgebras relative to a Chevalley group","authors":"Yutaka Yoshii","doi":"10.1142/s0219498825501853","DOIUrl":"https://doi.org/10.1142/s0219498825501853","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> be a simply connected and simple algebraic group defined and split over a finite prime field <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔽</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span><span></span> of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>p</mi></math></span><span></span> elements. In this paper, using an <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔽</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span><span></span>-linear map splitting Frobenius endomorphism on a hyperalgebra relative to <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>, we obtain some <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔽</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span><span></span>-linear isomorphisms induced by multiplication in the hyperalgebra.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150689","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 set of representatives and explicit factorization of xn − 1 over finite fields","authors":"Manjit Singh, Deepak","doi":"10.1142/s0219498825501701","DOIUrl":"https://doi.org/10.1142/s0219498825501701","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span> be a positive integer and let <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔽</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span><span></span> be a finite field with <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span> elements, where <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span> is a prime power and <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mo>gcd</mo><mo stretchy=\"false\">(</mo><mi>n</mi><mo>,</mo><mi>q</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mn>1</mn></math></span><span></span>. In this paper, we give the explicit factorization of <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup><mo stretchy=\"false\">−</mo><mn>1</mn></math></span><span></span> over <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔽</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span><span></span> and count the number of its irreducible factors for the following conditions: <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo>,</mo><mi>q</mi></math></span><span></span> are odd and <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext>rad</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>n</mi><mo stretchy=\"false\">)</mo><mo>|</mo><mo stretchy=\"false\">(</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=\"false\">+</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math></span><span></span>. First, we present a method to obtain the set of all representatives of <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span>-cyclotomic cosets modulo <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi></math></span><span></span>, where <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi><mo>=</mo><mo>gcd</mo><mo stretchy=\"false\">(</mo><mi>n</mi><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=\"false\">+</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math></span><span></span>. This set of representatives is then used to find the irreducible factors of <span><math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup><mo stretchy=\"false\">−</mo><mn>1</mn></math></span><span></span> and the cyclotomic polynomial <span><math altimg=\"eq-00016.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"normal\">Φ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo></math></span><span></span> over <span><math altimg=\"eq-00017.gif\" display=\"inline\" overflow=\"scroll","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150687","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":"Weak Hopf algebras, smash products and applications to adjoint-stable algebras","authors":"Zhimin Liu, Shenglin Zhu","doi":"10.1142/s0219498825501567","DOIUrl":"https://doi.org/10.1142/s0219498825501567","url":null,"abstract":"<p>For a semisimple quasi-triangular Hopf algebra <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>H</mi><mo>,</mo><mi>R</mi><mo stretchy=\"false\">)</mo></math></span><span></span> over a field <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi></math></span><span></span> of characteristic zero, and a strongly separable quantum commutative <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>H</mi></math></span><span></span>-module algebra <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>A</mi></math></span><span></span>, we show that <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>A</mi><mi>#</mi><mi>H</mi></math></span><span></span> is a weak Hopf algebra, and it can be embedded into a weak Hopf algebra <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mo>End</mo><msup><mrow><mi>A</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup><mo stretchy=\"false\">⊗</mo><mi>H</mi></math></span><span></span>. With these structures, <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow></mrow><mrow><mi>A</mi><mi>#</mi><mi>H</mi></mrow></msub><mo>Mod</mo></math></span><span></span> is the monoidal category introduced by Cohen and Westreich, and <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow></mrow><mrow><mo>End</mo><msup><mrow><mi>A</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup><mo stretchy=\"false\">⊗</mo><mi>H</mi></mrow></msub><mi mathvariant=\"cal\">ℳ</mi></math></span><span></span> is tensor equivalent to <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow></mrow><mrow><mi>H</mi></mrow></msub><mi mathvariant=\"cal\">ℳ</mi></math></span><span></span>. If <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>A</mi></math></span><span></span> is in the Müger center of <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow></mrow><mrow><mi>H</mi></mrow></msub><mi mathvariant=\"cal\">ℳ</mi></math></span><span></span>, then the embedding is a quasi-triangular weak Hopf algebra morphism. This explains the presence of a subgroup inclusion in the characterization of irreducible Yetter–Drinfeld modules for a finite group algebra.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156528","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":"Cohomology of modified Rota–Baxter Leibniz algebra of weight λ","authors":"Bibhash Mondal, Ripan Saha","doi":"10.1142/s0219498825501579","DOIUrl":"https://doi.org/10.1142/s0219498825501579","url":null,"abstract":"<p>Rota–Baxter operators have been paid much attention in the last few decades as they have many applications in mathematics and physics. In this paper, our object of study is modified Rota–Baxter operators on Leibniz algebras. We investigate modified Rota–Baxter Leibniz algebras from the cohomological point of view. We study a one-parameter formal deformation theory of modified Rota–Baxter Leibniz algebras and define the associated deformation cohomology that controls the deformation. Finally, as an application, we characterize equivalence classes of abelian extensions in terms of second cohomology groups.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150603","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":"Kostant’s generating functions and Mckay–Slodowy correspondence","authors":"Naihuan Jing, Zhijun Li, Danxia Wang","doi":"10.1142/s0219498825501713","DOIUrl":"https://doi.org/10.1142/s0219498825501713","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>N</mi><mo>⊴</mo><mi>G</mi></math></span><span></span> be a pair of finite subgroups of <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mstyle><mtext mathvariant=\"normal\">SL</mtext></mstyle></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">(</mo><mi>ℂ</mi><mo stretchy=\"false\">)</mo></math></span><span></span> and <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>V</mi></math></span><span></span> a finite-dimensional fundamental <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>-module. We study Kostant’s generating functions for the decomposition of the <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mstyle><mtext mathvariant=\"normal\">SL</mtext></mstyle></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">(</mo><mi>ℂ</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-module <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow></msup><mo stretchy=\"false\">(</mo><mi>V</mi><mo stretchy=\"false\">)</mo></math></span><span></span> restricted to <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>N</mi><mo>◃</mo><mi>G</mi></math></span><span></span> in connection with the McKay–Slodowy correspondence. In particular, the classical Kostant formula was generalized to a uniform version of the Poincaré series for the symmetric invariants in which the multiplicities of any individual module in the symmetric algebra are completely determined.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156516","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":"Modularity conditions in leibniz algebras","authors":"P. Páez-Guillán, Salvatore Siciliano, D. Towers","doi":"10.1142/s0219498825501919","DOIUrl":"https://doi.org/10.1142/s0219498825501919","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139624040","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":"Directed partial orders on complex numbers and quaternions","authors":"Jingjing Ma","doi":"10.1142/s0219498825501890","DOIUrl":"https://doi.org/10.1142/s0219498825501890","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139624656","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":"Duplex Hecke algebras of type B","authors":"Yu Xie, An Zhang, Bin Shu","doi":"10.1142/s021949882550166x","DOIUrl":"https://doi.org/10.1142/s021949882550166x","url":null,"abstract":"<p>As a sequel to [C. Xue and A. Zhang, Doubled Hecke algebras and related quantum Schur duality, preprint (2021), arXiv:2108.07587[math.RT], accepted for publication in <i>Algebra Colloq.</i>], in this article we first introduce a so-called duplex Hecke algebras of type <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"sans-serif\"><mi>B</mi></mstyle></math></span><span></span> which is a <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>ℚ</mi><mo stretchy=\"false\">(</mo><mi>q</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-algebra associated with the Weyl group <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"script\">𝒲</mi><mo stretchy=\"false\">(</mo><mstyle mathvariant=\"sans-serif\"><mi>B</mi></mstyle><mo stretchy=\"false\">)</mo></math></span><span></span> of type <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"sans-serif\"><mi>B</mi></mstyle></math></span><span></span>, and symmetric groups <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔖</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span><span></span> for <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>l</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>m</mi></math></span><span></span>, satisfying some Hecke relations (see Definition 3.1). This notion originates from the degenerate duplex Hecke algebra arising from the course of study of a kind of Schur–Weyl duality of Levi-type (see [B. Shu and Y. Yao, On enhanced reductive groups (I): Enhanced Schur algebras and the dualities related to degenerate duplex Hecke algebras, with an appendix by B. Liu, submitted (2023)]), extending the duplex Hecke algebra of type <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"sans-serif\"><mi>A</mi></mstyle></math></span><span></span> arising from the related <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span>-Schur–Weyl duality of Levi-type (see [C. Xue and A. Zhang, Doubled Hecke algebras and related quantum Schur duality, preprint (2021), arXiv:2108.07587[math.RT], accepted for publication in <i>Algebra Colloq.</i>]). A duplex Hecke algebra of type <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"sans-serif\"><mi>B</mi></mstyle></math></span><span></span> admits natural representations on certain tensor spaces. We then establish a Levi-type <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span>-Schur–Weyl duality of type <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"sans-serif\"><mi>B</mi></mstyle></math></span><span></span>, which reveals the double centralizer property between such duplex Hecke algebras and <span><math altimg=\"eq-00014.g","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150688","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":"Two results on character codegrees","authors":"Yang Liu, Yong Yang","doi":"10.1142/s0219498825501580","DOIUrl":"https://doi.org/10.1142/s0219498825501580","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> be a finite group and <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">Irr</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo></math></span><span></span> be the set of irreducible characters of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>. The codegree of an irreducible character <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>χ</mi></math></span><span></span> of the group <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> is defined as <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">cod</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>χ</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mo>|</mo><mi>G</mi><mo>:</mo><mstyle><mtext mathvariant=\"normal\">ker</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>χ</mi><mo stretchy=\"false\">)</mo><mo>|</mo><mo stretchy=\"false\">/</mo><mi>χ</mi><mo stretchy=\"false\">(</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math></span><span></span>. In this paper, we study two topics related to the character codegrees. The first result is related to the prime graph of character codegrees and we show that the codegree prime graphs of several classes of groups can be characterized only by graph theoretical terms. The second result is about the <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>p</mi></math></span><span></span>-parts of the codegrees and character degrees.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156706","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}