T. Karadag , D. McPhate , P.S. Ocal , T. Oke , S. Witherspoon
{"title":"Corrigendum to “Gerstenhaber brackets on Hochschild cohomology of general twisted tensor products” [J. Pure Appl. Algebra 225 (2021) 106597]","authors":"T. Karadag , D. McPhate , P.S. Ocal , T. Oke , S. Witherspoon","doi":"10.1016/j.jpaa.2024.107788","DOIUrl":"10.1016/j.jpaa.2024.107788","url":null,"abstract":"<div><p>In our paper <span><span>[1]</span></span>, several maps in Section 4 were incorrect. We correct them here. This oversight does not affect any of the results in the paper.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001853/pdfft?md5=f3914aeca84f6e053d1400ff61214a2d&pid=1-s2.0-S0022404924001853-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142020406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Auslander–Bridger–Yoshino theory for complexes of finitely generated projective modules","authors":"Yuya Otake","doi":"10.1016/j.jpaa.2024.107790","DOIUrl":"10.1016/j.jpaa.2024.107790","url":null,"abstract":"<div><p>Let <em>R</em> be a two-sided noetherian ring. Auslander and Bridger developed a theory of projective stabilization of the category of finitely generated <em>R</em>-modules, which is called the stable module theory. Recently, Yoshino established a stable “complex” theory, i.e., a theory of a certain stabilization of the homotopy category of complexes of finitely generated projective <em>R</em>-modules. We introduce higher versions of several notions introduced by Yoshino, such as <sup>⁎</sup>torsionfreeness and <sup>⁎</sup>reflexivity. Also, we prove the Auslander–Bridger approximation theorem for complexes of finitely generated projective <em>R</em>-modules.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142122198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exotic fusion system on a subgroup of the monster","authors":"Patrick Serwene","doi":"10.1016/j.jpaa.2024.107792","DOIUrl":"10.1016/j.jpaa.2024.107792","url":null,"abstract":"<div><p>We prove that an exotic fusion system described by Grazian on a subgroup of the Monster group is block-exotic, thus proving that exotic and block-exotic fusion systems are the same for all <em>p</em>-groups with sectional rank 3, where <span><math><mi>p</mi><mo>≥</mo><mn>5</mn></math></span>.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001890/pdfft?md5=a5845e82761dbc8c9f3d1f505e011e99&pid=1-s2.0-S0022404924001890-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141939696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the structures of a monoid of triangular vector-permutation polynomials, its group of units and its induced group of permutations","authors":"Amr Ali Abdulkader Al-Maktry","doi":"10.1016/j.jpaa.2024.107789","DOIUrl":"10.1016/j.jpaa.2024.107789","url":null,"abstract":"<div><p>Let <span><math><mi>n</mi><mo>></mo><mn>1</mn></math></span> and let <em>R</em> be a commutative ring with identity <span><math><mn>1</mn><mo>≠</mo><mn>0</mn></math></span> and <span><math><mi>R</mi><msup><mrow><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></mrow><mrow><mi>n</mi></mrow></msup></math></span> the set of all <em>n</em>-tuples of polynomials of the form <span><math><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>∈</mo><mi>R</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span>. We call these <em>n</em>-tuples vector-polynomials. We define composition on <span><math><mi>R</mi><msup><mrow><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></mrow><mrow><mi>n</mi></mrow></msup></math></span> by<span><span><span><math><mover><mrow><mi>g</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>∘</mo><mover><mrow><mi>f</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mo>(</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>)</mo><mo>,</mo><mtext> where </mtext><mover><mrow><mi>f</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>,</mo><mover><mrow><mi>g</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mo>(</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>.</mo></math></span></span></span> In this paper, we investigate vector-polynomials of the form<span><span><span><math><mover><mrow><mi>f</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><m","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001865/pdfft?md5=005e28025f8b89bcf8a3dc94d2d79381&pid=1-s2.0-S0022404924001865-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141939645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tomohiro Okuma , Kei-ichi Watanabe , Ken-ichi Yoshida
{"title":"Gorensteinness for normal tangent cones of elliptic ideals","authors":"Tomohiro Okuma , Kei-ichi Watanabe , Ken-ichi Yoshida","doi":"10.1016/j.jpaa.2024.107791","DOIUrl":"10.1016/j.jpaa.2024.107791","url":null,"abstract":"<div><p>Let <em>A</em> be a two-dimensional excellent normal Gorenstein local domain. In this paper, we characterize elliptic ideals <span><math><mi>I</mi><mo>⊂</mo><mi>A</mi></math></span> for its normal tangent cone <span><math><mover><mrow><mi>G</mi></mrow><mo>‾</mo></mover><mo>(</mo><mi>I</mi><mo>)</mo></math></span> to be Gorenstein. Moreover, we classify all those ideals in a Gorenstein elliptic singularity in the characteristic zero case.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141964195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Chow theory of Quot schemes of locally free quotients","authors":"Qingyuan Jiang","doi":"10.1016/j.jpaa.2024.107782","DOIUrl":"10.1016/j.jpaa.2024.107782","url":null,"abstract":"<div><p>We prove a formula for the Chow groups of Quot schemes that resolve degeneracy loci of a map between vector bundles, under expected dimension conditions. This formula simultaneously generalizes the formulas for projective bundles, Grassmannian bundles, blowups, Cayley's trick, projectivizations, flops from Springer-type resolutions, and Grassmannian-type flips and flops. We also apply the formula to study the Chow groups of (i) blowups of determinantal ideals; (ii) moduli spaces of linear series on curves; and (iii) (nested) Hilbert schemes of points on surfaces.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141964194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the vanishing of (co)homology for modules admitting certain filtrations","authors":"Olgur Celikbas , Yongwei Yao","doi":"10.1016/j.jpaa.2024.107787","DOIUrl":"10.1016/j.jpaa.2024.107787","url":null,"abstract":"<div><p>We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations and generalize a theorem of Celikbas-Takahashi. Our work produces new classes of rigid and test modules, particularly over local rings of prime characteristic. Additionally, it provides applications in the study of torsion in tensor products of modules, including a conjecture of Huneke-Wiegand.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Versality for pairs","authors":"Runar Ile","doi":"10.1016/j.jpaa.2024.107779","DOIUrl":"10.1016/j.jpaa.2024.107779","url":null,"abstract":"<div><p>For a pair (algebra, module) with equidimensional and isolated singularity we establish the existence of a versal henselian deformation. Obstruction theory in terms of an André-Quillen cohomology for pairs is a central ingredient in the Artin theory used. In particular we give a long exact sequence relating the algebra cohomology and the module cohomology with the cohomology of the pair and define a Kodaira-Spencer class for pairs.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001762/pdfft?md5=821fe00dcb6b4297ead3668a0cb9c547&pid=1-s2.0-S0022404924001762-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141848290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalized NS-algebras","authors":"Cyrille Ospel , Florin Panaite , Pol Vanhaecke","doi":"10.1016/j.jpaa.2024.107784","DOIUrl":"10.1016/j.jpaa.2024.107784","url":null,"abstract":"<div><p>We generalize the notion of an NS-algebra, which was previously only considered for associative, Lie and Leibniz algebras, to arbitrary categories of binary algebras with one operation. We do this by defining these algebras using a bimodule property, as we did in our earlier work for defining the notions of a dendriform and tridendriform algebra for such categories of algebras. We show that several types of operators lead to NS-algebras: Nijenhuis operators, twisted Rota-Baxter operators and relative Rota-Baxter operators of arbitrary weight. We thus provide a general framework in which several known results and constructions for associative, Lie and Leibniz-NS-algebras are unified, along with some new examples and constructions that we also present.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A BV-algebra structure on Hochschild cohomology of the integral group ring of finitely generated Abelian groups","authors":"Diego Duarte , Andrés Angel","doi":"10.1016/j.jpaa.2024.107781","DOIUrl":"10.1016/j.jpaa.2024.107781","url":null,"abstract":"<div><p>We study a Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the group ring of finitely generated abelian groups. The Batalin-Vilkovisky algebra structure for finite abelian groups comes from the fact that the group ring of finite groups is a symmetric algebra, and the Batalin-Vilkovisky algebra structure for free abelian groups of finite rank comes from the fact that its group ring is a Calabi-Yau algebra.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001786/pdfft?md5=a4ba10d9b35f9dafa657db68b2a29b37&pid=1-s2.0-S0022404924001786-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141844098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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