Journal of Algebra最新文献

{"title":"Computing the F-pure threshold of flag varieties","authors":"Justin Fong","doi":"10.1016/j.jalgebra.2025.08.034","DOIUrl":"10.1016/j.jalgebra.2025.08.034","url":null,"abstract":"<div><div>We compute the <em>F</em>-pure threshold of the natural cone over flag varieties in characteristic <span><math><mi>p</mi><mo>&gt;</mo><mn>0</mn></math></span>. Our calculations are mainly focused on flag varieties that are arithmetically Gorenstein, but we offer some results in the non-Gorenstein case. Our goal is to determine the <em>a</em>-invariant of the cone. As a result, the <em>F</em>-pure thresholds we find are independent of the characteristic <em>p</em>, hence one immediately gets the value of the log canonical threshold of flags in characteristic 0 as well.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 244-268"},"PeriodicalIF":0.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119822","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 non-congruent numbers as multiples of non-congruent numbers","authors":"Shenxing Zhang","doi":"10.1016/j.jalgebra.2025.09.006","DOIUrl":"10.1016/j.jalgebra.2025.09.006","url":null,"abstract":"<div><div>Let <span><math><mi>n</mi><mo>=</mo><mi>P</mi><mi>Q</mi></math></span> be a square-free positive integer, where <em>P</em> is a product of primes congruent to <span><math><mn>1</mn><mspace></mspace><mrow><mi>mod</mi></mrow><mspace></mspace><mn>8</mn></math></span>, and <em>Q</em> is a non-congruent number with a trivial 2-primary Shafarevich-Tate group. Under certain conditions on the Legendre symbols <span><math><mo>(</mo><mfrac><mrow><mi>q</mi></mrow><mrow><mi>p</mi></mrow></mfrac><mo>)</mo></math></span> for primes <span><math><mi>p</mi><mo>|</mo><mi>P</mi><mo>,</mo><mi>q</mi><mo>|</mo><mi>Q</mi></math></span>, we establish a criterion characterizing when <em>n</em> is non-congruent with a minimal or a second minimal 2-primary Shafarevich-Tate group. We also provide a sufficient condition for <em>n</em> to be non-congruent with a larger 2-primary Shafarevich-Tate group. These results involve the class groups and tame kernels of quadratic fields.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 394-418"},"PeriodicalIF":0.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119720","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":"E-disjunctive inverse semigroups","authors":"Luna Elliott ,&nbsp;Alex Levine ,&nbsp;James Mitchell","doi":"10.1016/j.jalgebra.2025.08.041","DOIUrl":"10.1016/j.jalgebra.2025.08.041","url":null,"abstract":"<div><div>In this paper we provide an overview of the class of inverse semigroups <em>S</em> such that every non-trivial congruence on <em>S</em> relates at least one idempotent to a non-idempotent; such inverse semigroups are called <em>E-disjunctive</em>. This overview includes the study of the inverse semigroup theoretic structure of <em>E</em>-disjunctive semigroups; a large number of natural examples; some asymptotic results establishing the rarity of such inverse semigroups; and a general structure theorem for all inverse semigroups where the building blocks are <em>E</em>-disjunctive.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 292-344"},"PeriodicalIF":0.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119618","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":"Ideal approximation theory in extriangulated categories","authors":"R.R. Xu ,&nbsp;X.H. Fu ,&nbsp;B.J. Gao ,&nbsp;M.Y. Sun","doi":"10.1016/j.jalgebra.2025.08.035","DOIUrl":"10.1016/j.jalgebra.2025.08.035","url":null,"abstract":"<div><div>In the present article, ideal approximation theory is introduced in extriangulated categories. To this end, Salce's Lemma, Christensen's Lemma, and Wakamatsu's Lemma are introduced and proved in an extriangulated category. It is also shown that a finite intersection of special precovering (respectively, special preenveloping) ideals remains special precovering (respectively, special preenveloping). The results in this article show that extriangulated categories are the appropriate context for developing ideal approximation theory.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 446-476"},"PeriodicalIF":0.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156576","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":"Contraderived categories of CDG-modules","authors":"Leonid Positselski ,&nbsp;Jan Šťovíček","doi":"10.1016/j.jalgebra.2025.08.040","DOIUrl":"10.1016/j.jalgebra.2025.08.040","url":null,"abstract":"<div><div>For any CDG-ring <figure><img></figure>, we show that the homotopy category of graded-projective (left) CDG-modules over <figure><img></figure> is equivalent to the quotient category of the homotopy category of graded-flat CDG-modules by its full triangulated subcategory of flat CDG-modules. The <em>contraderived category</em> (<em>in the sense of Becker</em>) <figure><img></figure> is the common name for these two triangulated categories. We also prove that the classes of cotorsion and graded-cotorsion CDG-modules coincide, and the contraderived category of CDG-modules is equivalent to the homotopy category of graded-flat graded-cotorsion CDG-modules. Assuming the graded ring <span><math><msup><mrow><mi>B</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> to be graded right coherent, we show that the contraderived category <figure><img></figure> is compactly generated and its full subcategory of compact objects is anti-equivalent to the full subcategory of compact objects in the coderived category of right CDG-modules <figure><img></figure>. Specifically, the latter triangulated category is the idempotent completion of the absolute derived category of finitely presented right CDG-modules <figure><img></figure>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 566-654"},"PeriodicalIF":0.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156571","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":"The de Rham cohomology of covers with a cyclic p-Sylow subgroup","authors":"Jędrzej Garnek ,&nbsp;Aristides Kontogeorgis","doi":"10.1016/j.jalgebra.2025.08.032","DOIUrl":"10.1016/j.jalgebra.2025.08.032","url":null,"abstract":"<div><div>Let <em>X</em> be a smooth projective curve over a field <em>k</em> with an action of a finite group <em>G</em>. A well-known result of Chevalley and Weil describes the <span><math><mi>k</mi><mo>[</mo><mi>G</mi><mo>]</mo></math></span>-module structure of cohomologies of <em>X</em> in the case when the characteristic of <em>k</em> does not divide #<em>G</em>. It is unlikely that such a formula can be derived in the general case, since the representation theory of groups with non-cyclic <em>p</em>-Sylow subgroups is wild in characteristic <em>p</em>. The goal of this article is to show that when <em>G</em> has a cyclic <em>p</em>-Sylow subgroup, the <em>G</em>-structure of the de Rham cohomology of <em>X</em> is completely determined by the ramification data. In principle, this leads to new formulas in the spirit of Chevalley and Weil for such curves. We provide such an explicit description of the de Rham cohomology in the cases when <span><math><mi>G</mi><mo>=</mo><mi>Z</mi><mo>/</mo><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and when the <em>p</em>-Sylow subgroup of <em>G</em> is normal of order <em>p</em>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 151-178"},"PeriodicalIF":0.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145107400","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":"The center of modular shifted Yangians and parabolic generators","authors":"Hao Chang ,&nbsp;Hongmei Hu","doi":"10.1016/j.jalgebra.2025.08.031","DOIUrl":"10.1016/j.jalgebra.2025.08.031","url":null,"abstract":"<div><div>This paper is devoted to the study of the shifted Yangian <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>σ</mi><mo>)</mo></math></span> associated to the general linear Lie algebra <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> over a field of positive characteristic. We obtain an explicit description of the center <span><math><mi>Z</mi><mo>(</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>σ</mi><mo>)</mo><mo>)</mo></math></span> of <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>σ</mi><mo>)</mo></math></span> in terms of parabolic generators, showing that it is generated by its Harish-Chandra center and its <em>p</em>-center.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 195-228"},"PeriodicalIF":0.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109745","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":"Lower bounds for Seshadri constants on blow ups of P2","authors":"Cyril J. Jacob","doi":"10.1016/j.jalgebra.2025.08.030","DOIUrl":"10.1016/j.jalgebra.2025.08.030","url":null,"abstract":"<div><div>Let <span><math><mi>π</mi><mo>:</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>→</mo><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> be a blow up of <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> at <em>r</em> distinct points <span><math><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span>. We study lower bounds for Seshadri constants of ample line bundles on <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span>. First, we consider the case when the points lie on a curve of degree <span><math><mi>d</mi><mo>≤</mo><mn>3</mn></math></span>, and the case when <span><math><mi>r</mi><mo>≤</mo><mn>8</mn></math></span>. We then assume that the points are very general and show that <span><math><mi>ε</mi><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>)</mo><mo>≥</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> if the Strong SHGH conjecture is true.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 380-393"},"PeriodicalIF":0.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119721","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":"Elementary equivalence of endomorphism rings and automorphism groups of periodic Abelian groups","authors":"Elena Bunina","doi":"10.1016/j.jalgebra.2025.09.002","DOIUrl":"10.1016/j.jalgebra.2025.09.002","url":null,"abstract":"<div><div>In this paper, we prove that the endomorphism rings <span><math><mspace></mspace><mrow><mi>End</mi></mrow><mspace></mspace><mi>A</mi></math></span> and <span><math><mspace></mspace><mrow><mi>End</mi></mrow><mspace></mspace><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> of periodic infinite Abelian groups <em>A</em> and <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> are elementarily equivalent if and only if the endomorphism rings of their <em>p</em>-components are elementarily equivalent for all primes <em>p</em>. Additionally, we show that the automorphism groups <span><math><mspace></mspace><mrow><mi>Aut</mi></mrow><mspace></mspace><mi>A</mi></math></span> and <span><math><mspace></mspace><mrow><mi>Aut</mi></mrow><mspace></mspace><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> of periodic Abelian groups <em>A</em> and <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> that do not have 2-components and do not contain cocyclic <em>p</em>-components are elementarily equivalent if and only if, for any prime <em>p</em>, the corresponding <em>p</em>-components <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math></span> of <em>A</em> and <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> are equivalent in second-order logic if they are not reduced, and are equivalent in second-order logic bounded by the cardinalities of their basic subgroups if they are reduced. According to <span><span>[11]</span></span>, for such groups <em>A</em> and <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>, their automorphism groups are elementarily equivalent if and only if their endomorphism rings are elementarily equivalent, and the automorphism groups of the corresponding <em>p</em>-components for all primes <em>p</em> are elementarily equivalent.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 179-194"},"PeriodicalIF":0.8,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109744","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 A-groups with the same index set as a nilpotent group","authors":"Wei Zhou ,&nbsp;Ilya Gorshkov","doi":"10.1016/j.jalgebra.2025.09.003","DOIUrl":"10.1016/j.jalgebra.2025.09.003","url":null,"abstract":"<div><div>Let <em>G</em> be a finite group and <span><math><mi>N</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the set of conjugacy class sizes of <em>G</em>. For a prime <em>p</em>, let <span><math><mo>|</mo><mi>G</mi><mo>|</mo><msub><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msub></math></span> be the highest <em>p</em>-power dividing some element of <span><math><mi>N</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and define <span><math><mo>|</mo><mi>G</mi><mo>|</mo><mo>|</mo><mo>=</mo><msub><mrow><mi>Π</mi></mrow><mrow><mi>p</mi><mo>∈</mo><mi>π</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mo>|</mo><mi>G</mi><mo>|</mo><msub><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msub></math></span>. <em>G</em> is said to be an <em>A</em>-group if all its Sylow subgroups are abelian. We prove that if <em>G</em> is an <em>A</em>-group such that <span><math><mi>N</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> contains <span><math><mo>|</mo><mi>G</mi><mo>|</mo><msub><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msub></math></span> for every <span><math><mi>p</mi><mo>∈</mo><mi>π</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> as well as <span><math><mo>|</mo><mi>G</mi><mo>|</mo><mo>|</mo></math></span>, then <em>G</em> must be abelian. This result gives a positive answer to a question posed by Camina and Camina in 2006.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"686 ","pages":"Pages 836-844"},"PeriodicalIF":0.8,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105116","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}