Journal of Pure and Applied Algebra最新文献

Corrigendum and addendum to “Transitive permutation groups where nontrivial elements have at most two fixed points” [J. Pure Appl. Algebra 219(4) (2015) 729–759] “非平凡元最多有两个不动点的传递置换群”的勘误和补充[J]。纯粹的达成。代数219(4)(2015)729-759]

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-05-30 DOI: 10.1016/j.jpaa.2025.108006

Paula Hähndel, Rebecca Waldecker

引用次数: 0

The canonical ideal and the deformation theory of curves with automorphisms 具有自同构曲线的正则理想与变形理论

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-05-28 DOI: 10.1016/j.jpaa.2025.108002

Aristides Kontogeorgis, Alexios Terezakis

引用次数: 0

Polynomial differential systems with invariant algebraic curves of arbitrary degree formed by Legendre polynomials 具有由勒让德多项式构成的任意次不变代数曲线的多项式微分系统

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-05-28 DOI: 10.1016/j.jpaa.2025.108001

Jaume Llibre , Claudia Valls

{"title":"Polynomial differential systems with invariant algebraic curves of arbitrary degree formed by Legendre polynomials","authors":"Jaume Llibre , Claudia Valls","doi":"10.1016/j.jpaa.2025.108001","DOIUrl":"10.1016/j.jpaa.2025.108001","url":null,"abstract":"<div><div>In 1891 Poincaré asked: <em>Given</em> <span><math><mi>m</mi><mo>≥</mo><mn>2</mn></math></span><em>, is there a positive integer</em> <span><math><mi>M</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></span> <em>such that if a polynomial differential system of degree m has an invariant algebraic curve of degree</em> <span><math><mo>≥</mo><mi>M</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></span><em>, then it has a rational first integral?</em> Brunella and Mendes repeated the same open question in 2000, and Lins-Neto in 2002. Between the years 2001 and 2003 three different families of quadratic polynomial differential systems provided a negative answer to this question. One of the answers used the Hermite polynomials. Recently a new negative answer was provided for polynomial differential systems of arbitrary degree using the Laguerre polynomials.</div><div>In this paper we provide another new negative answer but using for first time the Legendre polynomials. So the orthogonal polynomials play a role in the Poincaré's question. Moreover we classify the phase portraits of these polynomial differential systems having invariant algebraic curves of arbitrary degree based on the Legendre polynomials.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 8","pages":"Article 108001"},"PeriodicalIF":0.7,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167248","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

Symmetric and exterior squares of hook representations 钩子表示的对称和外部正方形

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-05-27 DOI: 10.1016/j.jpaa.2025.108003

Szabolcs Mészáros , János Wolosz

引用次数: 0

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 , 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

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

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

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

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