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Minimal resolutions of lattice ideals 晶格理想的最小分辨率
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-07 DOI: 10.1016/j.jpaa.2025.107901
Yupeng Li , Ezra Miller , Erika Ordog
{"title":"Minimal resolutions of lattice ideals","authors":"Yupeng Li ,&nbsp;Ezra Miller ,&nbsp;Erika Ordog","doi":"10.1016/j.jpaa.2025.107901","DOIUrl":"10.1016/j.jpaa.2025.107901","url":null,"abstract":"<div><div>A canonical minimal free resolution of an arbitrary co-artinian lattice ideal over the polynomial ring is constructed over any field whose characteristic is 0 or any but finitely many positive primes. The differential has a closed-form combinatorial description as a sum over lattice paths in <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> of weights that come from sequences of faces in simplicial complexes indexed by lattice points. Over a field of any characteristic, a non-canonical but simpler resolution is constructed by selecting choices of higher-dimensional analogues of spanning trees along lattice paths. These constructions generalize sylvan resolutions for monomial ideals by lifting them equivariantly to lattice modules.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 3","pages":"Article 107901"},"PeriodicalIF":0.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437093","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}
引用次数: 0
Steenrod closed parameter ideals in the mod-2 cohomology of A4 and SO(3) A4与SO(3)模2上同调中的Steenrod闭参数理想
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107899
Henrik Rüping , Marc Stephan , Ergün Yalçın
{"title":"Steenrod closed parameter ideals in the mod-2 cohomology of A4 and SO(3)","authors":"Henrik Rüping ,&nbsp;Marc Stephan ,&nbsp;Ergün Yalçın","doi":"10.1016/j.jpaa.2025.107899","DOIUrl":"10.1016/j.jpaa.2025.107899","url":null,"abstract":"<div><div>In this paper, we classify the parameter ideals in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> and in the Dickson algebra <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions <span><math><mi>n</mi><mo>,</mo><mi>m</mi></math></span> for which <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> (and <span><math><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span>) can act freely on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107899"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387715","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}
引用次数: 0
On pyramidal groups of prime power degree 关于素幂次的金字塔群
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107868
Xiaofang Gao , Martino Garonzi
{"title":"On pyramidal groups of prime power degree","authors":"Xiaofang Gao ,&nbsp;Martino Garonzi","doi":"10.1016/j.jpaa.2025.107868","DOIUrl":"10.1016/j.jpaa.2025.107868","url":null,"abstract":"<div><div>A Kirkman Triple System Γ is called <em>m</em>-pyramidal if there exists a subgroup <em>G</em> of the automorphism group of Γ that fixes <em>m</em> points and acts regularly on the other points. Such group <em>G</em> admits a unique conjugacy class <em>C</em> of involutions (elements of order 2) and <span><math><mo>|</mo><mi>C</mi><mo>|</mo><mo>=</mo><mi>m</mi></math></span>. We call groups with this property <em>m</em>-pyramidal. We prove that, if <em>m</em> is an odd prime power <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span>, with <span><math><mi>p</mi><mo>≠</mo><mn>7</mn></math></span>, then every <em>m</em>-pyramidal group is solvable if and only if either <span><math><mi>m</mi><mo>=</mo><mn>9</mn></math></span> or <em>k</em> is odd. The primitive permutation groups play an important role in the proof. We also determine the orders of the <em>m</em>-pyramidal groups when <em>m</em> is a prime number.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107868"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163678","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}
引用次数: 0
Categories of sets with infinite addition 具有无穷加法的集合的范畴
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107872
Pablo Andrés-Martínez , Chris Heunen
{"title":"Categories of sets with infinite addition","authors":"Pablo Andrés-Martínez ,&nbsp;Chris Heunen","doi":"10.1016/j.jpaa.2025.107872","DOIUrl":"10.1016/j.jpaa.2025.107872","url":null,"abstract":"<div><div>We consider sets with infinite addition, called Σ-monoids, and contribute to their literature in three ways. First, our definition subsumes those from previous works and allows us to relate them in terms of adjuctions between their categories. In particular, we discuss Σ-monoids with additive inverses. Second, we show that every Hausdorff commutative monoid is a Σ-monoid, and that there is a free Hausdorff commutative monoid for each Σ-monoid. Third, we prove that Σ-monoids have well-defined tensor products, unlike topological abelian groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107872"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163681","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}
引用次数: 0
Retraction notice to “Corrigendum to ‘On the fifth Singer algebraic transfer in a generic family of internal degree characterized by μ(n)=4’ [J. Pure Appl. Algebra 228 (2024) 107658]” 关于μ(n)=4的内阶一般族的第五Singer代数迁移的更正[J]。纯粹的达成。代数228 (2024)107658]
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107908
Đặng Võ Phúc
{"title":"Retraction notice to “Corrigendum to ‘On the fifth Singer algebraic transfer in a generic family of internal degree characterized by μ(n)=4’ [J. Pure Appl. Algebra 228 (2024) 107658]”","authors":"Đặng Võ Phúc","doi":"10.1016/j.jpaa.2025.107908","DOIUrl":"10.1016/j.jpaa.2025.107908","url":null,"abstract":"","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107908"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508436","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}
引用次数: 0
Combinatorial model categories are equivalent to presentable quasicategories 组合模型类别等同于可呈现的准类别
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2024.107860
Dmitri Pavlov
{"title":"Combinatorial model categories are equivalent to presentable quasicategories","authors":"Dmitri Pavlov","doi":"10.1016/j.jpaa.2024.107860","DOIUrl":"10.1016/j.jpaa.2024.107860","url":null,"abstract":"<div><div>We establish a Dwyer–Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable <span><math><mo>(</mo><mi>∞</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-categories. This implies that the underlying quasicategories of these relative categories are also equivalent. This article is also available at <span><span>arXiv:2110.04679v3</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107860"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162773","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}
引用次数: 0
Intermediate categories for proper abelian subcategories 适当阿贝尔子范畴的中间范畴
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107892
Anders S. Kortegaard
{"title":"Intermediate categories for proper abelian subcategories","authors":"Anders S. Kortegaard","doi":"10.1016/j.jpaa.2025.107892","DOIUrl":"10.1016/j.jpaa.2025.107892","url":null,"abstract":"<div><div>Let <span><math><mi>A</mi></math></span> be an extension-closed proper abelian subcategory of a triangulated category <span><math><mi>T</mi></math></span>, with no negative 1 and 2 extensions. From this, two functors from <span><math><mi>Σ</mi><mi>A</mi><mo>⁎</mo><mi>A</mi></math></span> to <span><math><mi>A</mi></math></span> can be constructed giving a snake lemma mirroring that of homology without needing a t-structure.</div><div>We generalize the concept of intermediate categories, which originates from a paper by Enomoto and Saito, to the setting of proper abelian subcategories and show that under certain assumptions this collection is in bijection with torsion-free classes in <span><math><mi>A</mi></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107892"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162793","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}
引用次数: 0
On the conjugacy separability of ordinary and generalized Baumslag–Solitar groups 关于普通和广义baumslag -孤群的共轭可分性
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107906
E.V. Sokolov
{"title":"On the conjugacy separability of ordinary and generalized Baumslag–Solitar groups","authors":"E.V. Sokolov","doi":"10.1016/j.jpaa.2025.107906","DOIUrl":"10.1016/j.jpaa.2025.107906","url":null,"abstract":"<div><div>Let <span><math><mi>C</mi></math></span> be a class of groups. A group <em>X</em> is said to be residually a <span><math><mi>C</mi></math></span>-group (conjugacy <span><math><mi>C</mi></math></span>-separable) if, for any elements <span><math><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>X</mi></math></span> that are not equal (not conjugate in <em>X</em>), there exists a homomorphism <em>σ</em> of <em>X</em> onto a group from <span><math><mi>C</mi></math></span> such that the elements <em>xσ</em> and <em>yσ</em> are still not equal (respectively, not conjugate in <em>Xσ</em>). A generalized Baumslag–Solitar group or GBS-group is the fundamental group of a finite connected graph of groups whose vertex and edge groups are all infinite cyclic. An ordinary Baumslag–Solitar group is the GBS-group that corresponds to a graph containing only one vertex and one loop. Suppose that the class <span><math><mi>C</mi></math></span> consists of periodic groups and is closed under taking subgroups and unrestricted wreath products. We prove that a non-solvable GBS-group is conjugacy <span><math><mi>C</mi></math></span>-separable if and only if it is residually a <span><math><mi>C</mi></math></span>-group. We also find a criterion for a solvable GBS-group to be conjugacy <span><math><mi>C</mi></math></span>-separable. As a corollary, we prove that an arbitrary GBS-group is conjugacy (finite) separable if and only if it is residually finite.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107906"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394582","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}
引用次数: 0
Generalizations of noncommutative Noether's problem 非交换诺特问题的推广
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107896
João Fernando Schwarz
{"title":"Generalizations of noncommutative Noether's problem","authors":"João Fernando Schwarz","doi":"10.1016/j.jpaa.2025.107896","DOIUrl":"10.1016/j.jpaa.2025.107896","url":null,"abstract":"<div><div>Noether's problem is a classical and very important problem in algebra. It is an intrinsically interesting problem in invariant theory, but with far reaching applications in the sutdy of moduli spaces, PI-algebras, and the Inverse problem of Galois theory, among others. To obtain a noncommutative analogue of Noether's problem, one would need a significant skew field that shares a role similar to the field of rational functions. Given the importance of the Weyl fields due to Gelfand-Kirillov's Conjecture, in 2006 J. Alev and F. Dumas introduced what is nowadays called the Noncommutative Noether's problem. The aim of this article is to generalize the main result of <span><span>[12]</span></span> for more general versions of Noether's problem; and consider its analogue in prime characteristic.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107896"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143351953","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}
引用次数: 0
Genus bound of curves on surfaces of almost minimal degree 几乎最小次曲面上曲线的属界
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107891
Wanseok Lee , Euisung Park
{"title":"Genus bound of curves on surfaces of almost minimal degree","authors":"Wanseok Lee ,&nbsp;Euisung Park","doi":"10.1016/j.jpaa.2025.107891","DOIUrl":"10.1016/j.jpaa.2025.107891","url":null,"abstract":"<div><div>Let <span><math><mi>C</mi><mo>⊂</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span>, <span><math><mi>r</mi><mo>≥</mo><mn>3</mn></math></span>, be a nondegenerate projective integral curve of degree <em>d</em> and arithmetic genus <em>g</em>. Castelnuovo theory says that<ul><li><span>(<em>i</em>)</span><span><div>if <span><math><mi>g</mi><mo>&gt;</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>d</mi><mo>,</mo><mi>r</mi><mo>)</mo></math></span> then <span><math><mi>C</mi></math></span> is contained in a surface of minimal degree, and</div></span></li><li><span>(<em>ii</em>)</span><span><div>if <span><math><mi>g</mi><mo>&gt;</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>d</mi><mo>,</mo><mi>r</mi><mo>)</mo></math></span> then <span><math><mi>C</mi></math></span> is contained in a surface of degree ≤<em>r</em>.</div></span></li></ul> In this paper, we prove that if <span><math><mi>g</mi><mo>&gt;</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>d</mi><mo>,</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mn>1</mn></math></span> then <span><math><mi>C</mi></math></span> is contained in a surface of minimal degree or a del Pezzo surface. To this aim, we show that <span><math><msub><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>d</mi><mo>,</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mn>1</mn></math></span> is the upper bound of <em>g</em> when <span><math><mi>C</mi></math></span> lies on a surface of degree <em>r</em> which is not a del Pezzo surface. We also provide a specific construction of curves with genus equal to the upper bound <span><math><msub><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>d</mi><mo>,</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107891"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162814","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}
引用次数: 0
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