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Journal of Pure and Applied Algebra最新文献

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Quantifier-free formulas and quantifier alternation depth in doctrines 无量词公式与量词交替的理论深度
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-27 DOI: 10.1016/j.jpaa.2025.108004
Marco Abbadini , Francesca Guffanti
{"title":"Quantifier-free formulas and quantifier alternation depth in doctrines","authors":"Marco Abbadini ,&nbsp;Francesca Guffanti","doi":"10.1016/j.jpaa.2025.108004","DOIUrl":"10.1016/j.jpaa.2025.108004","url":null,"abstract":"<div><div>This paper aims to incorporate the notion of quantifier-free formulas modulo a first-order theory and the stratification of formulas by quantifier alternation depth modulo a first-order theory into the algebraic treatment of classical first-order logic.</div><div>The set of quantifier-free formulas modulo a theory is axiomatized by what we call a <em>quantifier-free fragment</em> of a Boolean doctrine with quantifiers. Rather than being an intrinsic notion, a quantifier-free fragment is an additional structure on a Boolean doctrine with quantifiers. Under a smallness assumption, the structures occurring as quantifier-free fragments of some Boolean doctrine with quantifiers are precisely the Boolean doctrines (without quantifiers). In particular, every Boolean doctrine over a small category is a quantifier-free fragment of its quantifier completion.</div><div>Furthermore, the sequences obtained by stratifying an algebra of formulas by quantifier alternation depth modulo a theory are axiomatized by what we call <em>QA-stratified Boolean doctrines</em>. While quantifier-free fragments are defined in relation to an “ambient” Boolean doctrine with quantifiers, a QA-stratified Boolean doctrine requires no such ambient doctrine, and it consists of a sequence of Boolean doctrines (without quantifiers) with connecting axioms. QA-stratified Boolean doctrines are in one-to-one correspondence with pairs consisting of a Boolean doctrine with quantifiers and a quantifier-free fragment of it.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 8","pages":"Article 108004"},"PeriodicalIF":0.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167253","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
The Grothendieck group of a triangulated category 三角分类的格罗滕迪克群
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jpaa.2025.108005
Xiao-Wu Chen , Zhi-Wei Li , Xiaojin Zhang , Zhibing Zhao
{"title":"The Grothendieck group of a triangulated category","authors":"Xiao-Wu Chen ,&nbsp;Zhi-Wei Li ,&nbsp;Xiaojin Zhang ,&nbsp;Zhibing Zhao","doi":"10.1016/j.jpaa.2025.108005","DOIUrl":"10.1016/j.jpaa.2025.108005","url":null,"abstract":"<div><div>We give a direct proof of the following known result: the Grothendieck group of a triangulated category with a silting subcategory is isomorphic to the split Grothendieck group of the silting subcategory. Moreover, we obtain its cluster-tilting analogue.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 8","pages":"Article 108005"},"PeriodicalIF":0.7,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147341","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
Random unipotent Sylow subgroups of groups of Lie type of bounded rank 有界秩Lie型群的随机单幂Sylow子群
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jpaa.2025.108007
Saveliy V. Skresanov
{"title":"Random unipotent Sylow subgroups of groups of Lie type of bounded rank","authors":"Saveliy V. Skresanov","doi":"10.1016/j.jpaa.2025.108007","DOIUrl":"10.1016/j.jpaa.2025.108007","url":null,"abstract":"<div><div>In 2001 Liebeck and Pyber showed that a finite simple group of Lie type is a product of 25 carefully chosen unipotent Sylow subgroups. Later, in a series of works it was shown that 4 unipotent Sylow subgroups suffice. We prove that if the rank of a finite simple group of Lie type <em>G</em> is bounded, then <em>G</em> is a product of 11 random unipotent Sylow subgroups with probability tending to 1 as <span><math><mo>|</mo><mi>G</mi><mo>|</mo></math></span> tends to infinity. An application of the result to finite linear groups is given. The proofs do not depend on the classification of finite simple groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 8","pages":"Article 108007"},"PeriodicalIF":0.7,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167250","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
On the structure of finitely generated modules and the unmixed degrees 有限生成模块的结构与未混合度
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-16 DOI: 10.1016/j.jpaa.2025.108000
Nguyen Tu Cuong , Pham Hung Quy
{"title":"On the structure of finitely generated modules and the unmixed degrees","authors":"Nguyen Tu Cuong ,&nbsp;Pham Hung Quy","doi":"10.1016/j.jpaa.2025.108000","DOIUrl":"10.1016/j.jpaa.2025.108000","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>R</mi><mo>,</mo><mi>m</mi><mo>)</mo></math></span> be the homomorphic image of a Cohen-Macaulay local ring and <em>M</em> a finitely generated <em>R</em>-module. We use the splitting of local cohomology to shed a new light on the structure of non-Cohen-Macaulay modules. Namely, we show that every finitely generated <em>R</em>-module <em>M</em> is associated to a sequence of invariant modules. This module sequence expresses the deviation of <em>M</em> with the Cohen-Macaulay property. Our result generalizes the unmixed theorem of Cohen-Macaulayness for any finitely generated <em>R</em>-module. As an application we construct a new extended degree in the sense of Vasconcelos.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 108000"},"PeriodicalIF":0.7,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084257","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
Borel-type subalgebras of the lattice vertex operator algebra 格顶点算子代数的borel型子代数
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-16 DOI: 10.1016/j.jpaa.2025.107999
Jianqi Liu
{"title":"Borel-type subalgebras of the lattice vertex operator algebra","authors":"Jianqi Liu","doi":"10.1016/j.jpaa.2025.107999","DOIUrl":"10.1016/j.jpaa.2025.107999","url":null,"abstract":"<div><div>In this paper, we introduce and study new classes of sub-vertex operator algebras of the lattice vertex operator algebras (VOAs), which we call the conic, Borel, and parabolic-type subVOAs. These CFT-type VOAs, which are not necessarily strongly finitely generated, satisfy properties similar to the usual Borel and parabolic subalgebras of a Lie algebra. For the lowest-rank nontrivial example of Borel-type subVOA <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>B</mi></mrow></msub></math></span> of <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>Z</mi><mi>α</mi></mrow></msub></math></span>, we explicitly determine its Zhu's algebra <span><math><mi>A</mi><mo>(</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>)</mo></math></span> in terms of generators and relations.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107999"},"PeriodicalIF":0.7,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098469","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
Absolute algebras, contramodules, and duality squares 绝对代数，控制模和对偶平方
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-16 DOI: 10.1016/j.jpaa.2025.107998
Victor Roca i Lucio
{"title":"Absolute algebras, contramodules, and duality squares","authors":"Victor Roca i Lucio","doi":"10.1016/j.jpaa.2025.107998","DOIUrl":"10.1016/j.jpaa.2025.107998","url":null,"abstract":"<div><div>Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as algebras over cooperads. The goal of this article is to develop this new theory. First, we relate the homotopy theory of absolute algebras to the homotopy theory of usual algebras via a <em>duality square</em>. It intertwines bar-cobar adjunctions with linear duality adjunctions. In particular, we show that linear duality functors between types of coalgebras and types of algebras are Quillen functors and that they induce equivalences between objects with finiteness conditions on their homology. We give general comparison results between absolute types of algebras and their classical counterparts. We work out examples of this theory such as absolute associative algebras and absolute Lie algebras, and show that it includes the theory of contramodules. Finally, in <span><span>[9]</span></span>, the authors showed that two nilpotent Lie algebras whose universal enveloping algebras are isomorphic as associative algebras must be isomorphic. As an application of our results, we generalize their theorem to the setting of absolute Lie algebras and absolute <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107998"},"PeriodicalIF":0.7,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107715","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
On virtual resolutions of points in a product of two projective spaces 两个射影空间积中点的虚分辨率
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-16 DOI: 10.1016/j.jpaa.2025.107997
Isidora Bailly-Hall , Christine Berkesch , Karina Dovgodko , Sean Guan , Saisudharshan Sivakumar , Jishi Sun
{"title":"On virtual resolutions of points in a product of two projective spaces","authors":"Isidora Bailly-Hall ,&nbsp;Christine Berkesch ,&nbsp;Karina Dovgodko ,&nbsp;Sean Guan ,&nbsp;Saisudharshan Sivakumar ,&nbsp;Jishi Sun","doi":"10.1016/j.jpaa.2025.107997","DOIUrl":"10.1016/j.jpaa.2025.107997","url":null,"abstract":"<div><div>For finite sets of points in <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, we produce short virtual resolutions, as introduced by Berkesch, Erman, and Smith <span><span>[3]</span></span>. We first intersect with a sufficiently high power of one set of variables for points in <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> to produce a virtual resolution of length <span><math><mi>n</mi><mo>+</mo><mi>m</mi></math></span>. Then, we describe an explicit virtual resolution of length 3 for a set of points in sufficiently general position in <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, via a subcomplex of a free resolution. This first result generalizes to <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> work of Harada, Nowroozi, and Van Tuyl <span><span>[16]</span></span> and the second partially generalizes work of <span><span>[16]</span></span> and Booms-Peot <span><span>[5]</span></span>, which were both for <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. Along the way, we also note an explicit relationship between Betti numbers and higher difference matrices of bigraded Hilbert matrices for <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 8","pages":"Article 107997"},"PeriodicalIF":0.7,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144108076","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
From nonabelian basechange to basechange with coefficients 从非abel基交换到带系数基交换
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-15 DOI: 10.1016/j.jpaa.2025.107993
Peter J. Haine
{"title":"From nonabelian basechange to basechange with coefficients","authors":"Peter J. Haine","doi":"10.1016/j.jpaa.2025.107993","DOIUrl":"10.1016/j.jpaa.2025.107993","url":null,"abstract":"<div><div>The goal of this paper is to explain when basechange theorems for sheaves of spaces imply basechange for sheaves with coefficients in other presentable ∞-categories. We accomplish this by analyzing when the tensor product of presentable ∞-categories preserves left adjointable squares. As a sample result, we show that the Proper Basechange Theorem in topology holds with coefficients in any presentable ∞-category which is compactly generated or stable. We also prove results about the interaction between tensor products of presentable ∞-categories and various categorical constructions that are of independent interest. For example, we show that tensoring with a compactly generated presentable ∞-category preserves fully faithful or conservative left exact left adjoints. We also show that tensoring with a presentable ∞-category that is compactly generated or stable preserves recollements.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107993"},"PeriodicalIF":0.7,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107621","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
Torsion-free instanton sheaves on the blow-up of P3 at a point 无扭力瞬时轮轴在P3的某一点上爆炸
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-14 DOI: 10.1016/j.jpaa.2025.107992
Abdelmoubine Amar Henni
{"title":"Torsion-free instanton sheaves on the blow-up of P3 at a point","authors":"Abdelmoubine Amar Henni","doi":"10.1016/j.jpaa.2025.107992","DOIUrl":"10.1016/j.jpaa.2025.107992","url":null,"abstract":"<div><div>We study an extension of the instanton bundle's definition given by Casnati, Coskun, Genk, and Malaspina for Fano threefolds in order to include non locally-free ones on the blow-up <span><math><mover><mrow><msup><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow><mrow><mo>˜</mo></mrow></mover></math></span>, of the projective 3-space at a point. Using the suggested definition, we show that any reflexive instanton sheaf must be locally free, and that the strictly torsion-free instanton sheaves have singularities of pure dimension 1. We construct examples and study their <em>μ</em>-stability. Additionally, we find that these sheaves contribute to the (partial) compactification of the 't Hooft component of the moduli space of instantons, on <span><math><mover><mrow><msup><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow><mrow><mo>˜</mo></mrow></mover></math></span>. In particular, our non locally-free examples are shown to be smooth and smoothable.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107992"},"PeriodicalIF":0.7,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144088839","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
Quasi-Hopf algebras of dimension 6 6维的拟hopf代数
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-08 DOI: 10.1016/j.jpaa.2025.107991
D. Bulacu , M. Misurati
{"title":"Quasi-Hopf algebras of dimension 6","authors":"D. Bulacu ,&nbsp;M. Misurati","doi":"10.1016/j.jpaa.2025.107991","DOIUrl":"10.1016/j.jpaa.2025.107991","url":null,"abstract":"<div><div>We complete the classification of the 6-dimensional quasi-Hopf algebras, by proving that any such algebra is semisimple. As byproducts, we provide examples of 6-dimensional quasi-bialgebras that are not semisimple as algebras, as well as the concrete quasi-Hopf structures of the 6-dimensional semisimple quasi-Hopf algebras previously classified by Etingof and Gelaki in terms of their category of representations. In total there are 15 quasi-Hopf algebras in dimension 6 which are not pairwise twist equivalent.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107991"},"PeriodicalIF":0.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069947","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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