Journal of Pure and Applied Algebra最新文献_第4页

Common divisor graphs for skew braces

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107876

Silvia Properzi , Arne Van Antwerpen

引用次数: 0

On the finite spaces of non-trivial proper subgroups of finite groups

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107894

Lingling Han, Tao Zheng

引用次数: 0

Δ-locally nilpotent algebras, their ideal structure and simplicity criteria

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2024.107861

V.V. Bavula

{"title":"Δ-locally nilpotent algebras, their ideal structure and simplicity criteria","authors":"V.V. Bavula","doi":"10.1016/j.jpaa.2024.107861","DOIUrl":"10.1016/j.jpaa.2024.107861","url":null,"abstract":"<div><div>The class of Δ-locally nilpotent algebras introduced in the paper is a wide generalization of the algebras of differential operators on commutative algebras. Examples include all the rings <math><mi>D</mi><mo>(</mo><mi>A</mi><mo>)</mo></math> of differential operators on commutative algebras in arbitrary characteristic, all subalgebras of <math><mi>D</mi><mo>(</mo><mi>A</mi><mo>)</mo></math> that contain the algebra A, the universal enveloping algebras of nilpotent, solvable and semi-simple Lie algebras, the Poisson universal enveloping algebra of an arbitrary Poisson algebra, iterated Ore extensions <math><mi>A</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><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>δ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math>, certain generalized Weyl algebras, and others.</div><div>In [8], simplicity criteria are given for the algebras differential operators on commutative algebras. To find the simplicity criterion was a long standing problem from 60'th. The aim of the paper is to describe the ideal structure of Δ-locally nilpotent algebras and as a corollary to give simplicity criteria for them. These results are generalizations of the results of [8]. Examples are considered.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107861"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163664","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

Classification of G2-orbits for pairs of octonions

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107875

Artem Lopatin , Alexandr N. Zubkov

引用次数: 0

Semi-galois Categories I: The classical Eilenberg variety theory

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107863

Takeo Uramoto

{"title":"Semi-galois Categories I: The classical Eilenberg variety theory","authors":"Takeo Uramoto","doi":"10.1016/j.jpaa.2025.107863","DOIUrl":"10.1016/j.jpaa.2025.107863","url":null,"abstract":"<div><div>This paper is an extended version of our proceedings paper [49] announced at LICS'16; in order to complement it, this version is written from a different viewpoint including topos-theoretic aspects of [49] that were not discussed there. Technically, this paper introduces and studies the class of semi-galois categories, which extend galois categories and are dual to profinite monoids in the same way as galois categories are dual to profinite groups; the study on this class of categories is aimed at providing an axiomatic reformulation of Eilenberg's theory of varieties of regular languages—a branch in formal language theory that has been developed since the mid 1960s and particularly concerns systematic classification of regular languages, finite monoids and deterministic finite automata. In this paper, detailed proofs of our central results announced at LICS'16 are presented, together with topos-theoretic considerations. The main results include (I) a proof of the duality theorem between profinite monoids and semi-galois categories, extending the duality theorem between profinite groups and galois categories; based on these results on semi-galois categories we then discuss (II) a reinterpretation of Eilenberg's theory from a viewpoint of the duality theorem; in relation with this reinterpretation of the theory, (III) we also give a purely topos-theoretic characterization of classifying topoi <math><mi>B</mi><mi>M</mi></math> of profinite monoids M among general coherent topoi, which is a topos-theoretic application of (I). This characterization states that a topos <math><mi>E</mi></math> is equivalent to the classifying topos <math><mi>B</mi><mi>M</mi></math> of some profinite monoid M if and only if <math><mi>E</mi></math> is (i) coherent, (ii) noetherian, and (iii) has a surjective coherent point <math><mi>p</mi><mo>:</mo><mrow><mi>Sets</mi></mrow><mo>→</mo><mi>E</mi></math>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107863"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163676","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

Toric splittings

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107870

Anargyros Katsabekis, Apostolos Thoma

引用次数: 0

On the derived category of a toric stack bundle

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107882

Qian Chao , Jiun-Cheng Chen , Hsian-Hua Tseng

引用次数: 0

Exact weights and path metrics for triangulated categories and the derived category of persistence modules

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107903

Peter Bubenik , José A. Vélez-Marulanda

{"title":"Exact weights and path metrics for triangulated categories and the derived category of persistence modules","authors":"Peter Bubenik , José A. Vélez-Marulanda","doi":"10.1016/j.jpaa.2025.107903","DOIUrl":"10.1016/j.jpaa.2025.107903","url":null,"abstract":"<div><div>We define exact weights on a pretriangulated category to be nonnegative functions on objects satisfying a subadditivity condition with respect to distinguished triangles. Such weights induce a metric on objects in the category, which we call a path metric. Our exact weights generalize the rank functions of J. Chuang and A. Lazarev for triangulated categories and are analogous to the exact weights for an exact category given by the first author and J. Scott and D. Stanley. We show that (co)homological functors from a triangulated category to an abelian category with an additive weight induce an exact weight on the triangulated category. We prove that triangle equivalences induce an isometry for the path metrics induced by cohomological functors. In the perfectly generated or compactly generated case, we use Brown representability to express the exact weight on the triangulated category. We give three characterizations of exactness for a weight on a pretriangulated category and show that they are equivalent. We also define Wasserstein distances for triangulated categories. Finally, we apply our work to derived categories of persistence modules and to representations of continuous quivers of type <math><mi>A</mi></math>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107903"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394581","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

Schur powers of the cokernel of a graded morphism

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107902

Jan O. Kleppe , Rosa M. Miró-Roig

{"title":"Schur powers of the cokernel of a graded morphism","authors":"Jan O. Kleppe , Rosa M. Miró-Roig","doi":"10.1016/j.jpaa.2025.107902","DOIUrl":"10.1016/j.jpaa.2025.107902","url":null,"abstract":"<div><div>Let <math><mi>φ</mi><mo>:</mo><mi>F</mi><mo>⟶</mo><mi>G</mi></math> be a graded morphism between free R-modules of rank t and <math><mi>t</mi><mo>+</mo><mi>c</mi><mo>−</mo><mn>1</mn></math>, respectively, and let <math><msub><mrow><mi>I</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>(</mo><mi>φ</mi><mo>)</mo></math> be the ideal generated by the <math><mi>j</mi><mo>×</mo><mi>j</mi></math> minors of a matrix representing φ. In this paper: (1) We show that the canonical module of <math><mi>R</mi><mo>/</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>(</mo><mi>φ</mi><mo>)</mo></math> is up to twist equal to a suitable Schur power <math><msup><mrow><mi>Σ</mi></mrow><mrow><mi>I</mi></mrow></msup><mi>M</mi></math> of <math><mi>M</mi><mo>=</mo><mi>coker</mi><mo>(</mo><msup><mrow><mi>φ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></math>; thus equal to <math><msup><mrow><mo>∧</mo></mrow><mrow><mi>t</mi><mo>+</mo><mn>1</mn><mo>−</mo><mi>j</mi></mrow></msup><mi>M</mi></math> if <math><mi>c</mi><mo>=</mo><mn>2</mn></math> in which case we find a minimal free R-resolution of <math><msup><mrow><mo>∧</mo></mrow><mrow><mi>t</mi><mo>+</mo><mn>1</mn><mo>−</mo><mi>j</mi></mrow></msup><mi>M</mi></math> for any j, (2) For <math><mi>c</mi><mo>=</mo><mn>3</mn></math>, we construct a free R-resolution of <math><msup><mrow><mo>∧</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>M</mi></math> which starts almost minimally (i.e. the first three terms are minimal up to a precise summand), and (3) For <math><mi>c</mi><mo>≥</mo><mn>4</mn></math>, we construct under a certain depth condition the first three terms of a free R-resolution of <math><msup><mrow><mo>∧</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>M</mi></math> which are minimal up to a precise summand. As a byproduct we answer the first open case of a question posed by Buchsbaum and Eisenbud in [2, pg. 299].</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107902"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420767","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

Matrix invertible extensions over commutative rings. Part I: General theory

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107852

Grigore Călugăreanu , Horia F. Pop , Adrian Vasiu

{"title":"Matrix invertible extensions over commutative rings. Part I: General theory","authors":"Grigore Călugăreanu , Horia F. Pop , Adrian Vasiu","doi":"10.1016/j.jpaa.2024.107852","DOIUrl":"10.1016/j.jpaa.2024.107852","url":null,"abstract":"<div><div>A unimodular <math><mn>2</mn><mo>×</mo><mn>2</mn></math> matrix with entries in a commutative R is called extendable (resp. simply extendable) if it extends to an invertible <math><mn>3</mn><mo>×</mo><mn>3</mn></math> matrix (resp. invertible <math><mn>3</mn><mo>×</mo><mn>3</mn></math> matrix whose <math><mo>(</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math> entry is 0). We obtain necessary and sufficient conditions for a unimodular <math><mn>2</mn><mo>×</mo><mn>2</mn></math> matrix to be extendable (resp. simply extendable) and use them to study the class <math><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub></math> (resp. <math><mi>S</mi><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub></math>) of rings R with the property that all unimodular <math><mn>2</mn><mo>×</mo><mn>2</mn></math> matrices with entries in R are extendable (resp. simply extendable). We also study the larger class <math><msub><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow></msub></math> of rings R with the property that all unimodular <math><mn>2</mn><mo>×</mo><mn>2</mn></math> matrices of determinant 0 and with entries in R are (simply) extendable (e.g., rings with trivial Picard groups or pre-Schreier domains). Among Dedekind domains, polynomial rings over <math><mi>Z</mi></math> and Hermite rings, only the EDRs belong to the class <math><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub></math> or <math><mi>S</mi><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub></math>. If R has stable range at most 2 (e.g., R is a Hermite ring or <math><mi>dim</mi><mo>⁡</mo><mo>(</mo><mi>R</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math>), then R is an <math><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub></math> ring iff it is an <math><mi>S</mi><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub></math> ring.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107852"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143094014","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