Journal of Algebra and Its Applications最新文献

{"title":"Morita equivalence and globalization for partial Hopf actions on nonunital algebras","authors":"Marcelo Muniz Alves, Tiago Luiz Ferrazza","doi":"10.1142/s0219498825502627","DOIUrl":"https://doi.org/10.1142/s0219498825502627","url":null,"abstract":"<p>In this work, we investigate partial actions of a Hopf algebra <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>H</mi></math></span><span></span> on nonunital algebras and the associated partial smash products, with the objective of providing a framework where one may obtain results for both <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mo>𝕜</mo></math></span><span></span>-algebras with local units and <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mo>𝕜</mo></math></span><span></span>-categories. We show that our partial actions correspond to nonunital algebras in the category of partial representations of <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>H</mi></math></span><span></span>. The central problem of existence of a globalization for a partial action is studied in detail, and we provide sufficient conditions for the existence (and uniqueness) of a minimal globalization for associative algebras in general. Extending previous results by Abadie, Dokuchaev, Exel and Simon, we define Morita equivalence for partial Hopf actions, and we show that if two symmetrical partial actions are Morita equivalent then their standard globalizations are also Morita equivalent. Particularizing to the case of a partial action on an algebra with local units, we obtain several strong results on equivalences of categories of modules of partial smash products of algebras and partial smash products of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mo>𝕜</mo></math></span><span></span>-categories.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152442","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":"Wilf inequality is preserved under gluing of semigroups","authors":"Srishti Singh, Hema Srinivasan","doi":"10.1142/s021949882550255x","DOIUrl":"https://doi.org/10.1142/s021949882550255x","url":null,"abstract":"<p>Wilf Conjecture on numerical semigroups is a question posed by Wilf in 1978 and is an inequality connecting the Frobenius number, embedding dimension and the genus of the semigroup. The conjecture is still open in general. We prove that this Wilf inequality is preserved under gluing of numerical semigroups. If the numerical semigroups minimally generated by <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>A</mi><mo>=</mo><mo stretchy=\"false\">{</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>p</mi></mrow></msub><mo stretchy=\"false\">}</mo></math></span><span></span> and <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>B</mi><mo>=</mo><mo stretchy=\"false\">{</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>q</mi></mrow></msub><mo stretchy=\"false\">}</mo></math></span><span></span> satisfy the Wilf inequality, then so does their gluing which is minimally generated by <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi><mo>=</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>A</mi><mo stretchy=\"false\">⊔</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>B</mi></math></span><span></span>. We discuss the extended Wilf’s Conjecture in higher dimensions for certain affine semigroups and prove an analogous result.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811111","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":"Graver bases of shifted numerical semigroups with 3 generators","authors":"James Howard, Christopher O’Neill","doi":"10.1142/s0219498825502275","DOIUrl":"https://doi.org/10.1142/s0219498825502275","url":null,"abstract":"<p>A numerical semigroup <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>M</mi></math></span><span></span> is a subset of the non-negative integers that is closed under addition. A factorization of <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo>∈</mo><mi>M</mi></math></span><span></span> is an expression of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span> as a sum of generators of <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>M</mi></math></span><span></span>, and the Graver basis of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>M</mi></math></span><span></span> is a collection <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">Gr</mtext></mstyle><mo stretchy=\"false\">(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>t</mi></mrow></msub><mo stretchy=\"false\">)</mo></math></span><span></span> of trades between the generators of <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>M</mi></math></span><span></span> that allows for efficient movement between factorizations. Given positive integers <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span><span></span>, consider the family <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>M</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo stretchy=\"false\">〈</mo><mi>t</mi><mo stretchy=\"false\">+</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><mi>t</mi><mo stretchy=\"false\">+</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span><span></span> of “shifted” numerical semigroups whose generators are obtained by translating <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span><span></span> by an integer parameter <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>t</mi></math></span><span></span>. In this paper, we characterize the Graver basis <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">Gr</mtext></mstyle><mo stretchy=\"false\">(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>t</mi></mrow></msub><mo stretchy=\"false\">)</mo></math></span><span></span> of <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>M</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span><span></span> for sufficiently large <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><mi>t</mi></math></span><span></span> in the case ","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140634619","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 2-Absorbing Ideals Of Non-Commutative Semirings","authors":"Mohammad Adarbeh, Mohammad Saleh","doi":"10.1142/s0219498825502780","DOIUrl":"https://doi.org/10.1142/s0219498825502780","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140687556","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 Dual Vector Spaces of Symmetric Tensor Powers of Composition Algebras","authors":"A. Razon","doi":"10.1142/s0219498825502779","DOIUrl":"https://doi.org/10.1142/s0219498825502779","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140686453","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":"Relationships between Almost Completely Decomposable Abelian Groups and Their Multiplication Groups","authors":"E. Kompantseva, Askar Tuganbaev","doi":"10.1142/s0219498825502755","DOIUrl":"https://doi.org/10.1142/s0219498825502755","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140690445","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 the Graded Injective Hull of R/𝔭 in Prime Characteristic","authors":"Aarti Patle, Jyoti Singh","doi":"10.1142/s0219498825502810","DOIUrl":"https://doi.org/10.1142/s0219498825502810","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140686534","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 primeness of noncommutative polynomials on prime rings","authors":"M. Tamer Koşan, Tsiu-Kwen Lee","doi":"10.1142/s0219498825502767","DOIUrl":"https://doi.org/10.1142/s0219498825502767","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140688518","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 Boomerang Uniformity of Three Classes of Permutation Polynomials over 𝔽2n","authors":"Qian Liu, Zhixiong Chen, Ximeng Liu","doi":"10.1142/s0219498825502792","DOIUrl":"https://doi.org/10.1142/s0219498825502792","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140686316","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 and the controlling algebra of crossed homomorphisms on 3-Lie algebras","authors":"Shuai Hou, Meiyan Hu, Lina Song, Yanqiu Zhou","doi":"10.1142/s0219498825502317","DOIUrl":"https://doi.org/10.1142/s0219498825502317","url":null,"abstract":"<p>In this paper, first we give the notion of a crossed homomorphism on a <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mn>3</mn></math></span><span></span>-Lie algebra with respect to an action on another <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mn>3</mn></math></span><span></span>-Lie algebra, and characterize it using a homomorphism from a 3-Lie algebra to the semidirect product 3-Lie algebra. We also establish the relationship between crossed homomorphisms and relative Rota–Baxter operators of weight <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mn>1</mn></math></span><span></span> on 3-Lie algebras. Next we construct a cohomology theory for a crossed homomorphism on <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mn>3</mn></math></span><span></span>-Lie algebras and classify infinitesimal deformations of crossed homomorphisms using the second cohomology group. Finally, using the higher derived brackets, we construct an <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span><span></span>-algebra whose Maurer–Cartan elements are crossed homomorphisms. Consequently, we obtain the twisted <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span><span></span>-algebra that controls deformations of a given crossed homomorphism on <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mn>3</mn></math></span><span></span>-Lie algebras.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608944","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}