Journal of Algebra最新文献

{"title":"Corrigendum to “Conjugacy languages in virtual graph products” [J. Algebra 634 (2023) 873–910]","authors":"Gemma Crowe","doi":"10.1016/j.jalgebra.2025.09.026","DOIUrl":"10.1016/j.jalgebra.2025.09.026","url":null,"abstract":"","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 374-376"},"PeriodicalIF":0.8,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334827","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":"Determining the vertex stabilizers of 4-valent half-arc-transitive graphs","authors":"Binzhou Xia,&nbsp;Zhishuo Zhang,&nbsp;Sanming Zhou","doi":"10.1016/j.jalgebra.2025.09.021","DOIUrl":"10.1016/j.jalgebra.2025.09.021","url":null,"abstract":"<div><div>We say that a group is a 4-HAT-stabilizer if it is the vertex stabilizer of some connected 4-valent half-arc-transitive graph. In 2001, Marušič and Nedela proved that every 4-HAT-stabilizer must be a concentric group. However, over the past two decades, only a very small proportion of concentric groups have been shown to be 4-HAT-stabilizers. This paper develops a theory that provides a general framework for determining whether a concentric group is a 4-HAT-stabilizer. With this approach, we significantly extend the known list of 4-HAT-stabilizers. As a corollary, we confirm that <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>7</mn></mrow></msub><mo>×</mo><msubsup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>m</mi><mo>−</mo><mn>7</mn></mrow></msubsup></math></span> are 4-HAT-stabilizers for <span><math><mi>m</mi><mo>≥</mo><mn>7</mn></math></span>, achieving the goal of a conjecture posed by Spiga and Xia.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 307-343"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334823","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":"Arbitrary residual finiteness and conjugacy separability growth","authors":"Lukas Vandeputte","doi":"10.1016/j.jalgebra.2025.09.025","DOIUrl":"10.1016/j.jalgebra.2025.09.025","url":null,"abstract":"<div><div>In a recent paper, Henry Bradford showed that all sufficiently fast growing functions appear as the residual finiteness growth function of some group. In this paper we show that the groups there constructed are conjugacy separable and that their conjugacy separability growth is equal to the residual finiteness growth. It follows that all sufficiently fast growing functions appear as the conjugacy separability growth function of some group. We extend this construction to a new class of groups such that given functions <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> under the same constraints and satisfying <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≥</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, we can find a group such that the residual finiteness growth is given by <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and the conjugacy separability growth by <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, showing that the residual finiteness growth and conjugacy separability growth behave independently and can lie arbitrarily far apart.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 91-115"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334828","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":"Reality determining subgraphs and strongly real modules","authors":"Matheus Brito ,&nbsp;Adriano Moura ,&nbsp;Clayton Silva","doi":"10.1016/j.jalgebra.2025.09.023","DOIUrl":"10.1016/j.jalgebra.2025.09.023","url":null,"abstract":"<div><div>The concept of pseudo <em>q</em>-factorization graphs was recently introduced by the last two authors as a combinatorial language which is suited for capturing certain properties of Drinfeld polynomials. Using certain known representation theoretic facts about tensor products of Kirillov Reshetikhin modules and <em>q</em>-characters, combined with special topological/ combinatorial properties of the underlying <em>q</em>-factorization graphs, the last two authors showed that, for algebras of type <em>A</em>, modules associated to totally ordered graphs are prime, while those associated to trees are real. In this paper, we extend the latter result. We introduce the notions of strongly real modules and that of trees of modules satisfying certain properties. In particular, we can consider snake trees, i.e., trees formed from snake modules. Among other results, we show that a certain class of such generalized trees, which properly contains the snake trees, give rise to strongly real modules.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 244-283"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334844","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 algebraic and geometric classification of right alternative and semi-alternative algebras","authors":"Hani Abdelwahab ,&nbsp;Ivan Kaygorodov ,&nbsp;Roman Lubkov","doi":"10.1016/j.jalgebra.2025.09.019","DOIUrl":"10.1016/j.jalgebra.2025.09.019","url":null,"abstract":"<div><div>The algebraic and geometric classifications of complex 3-dimensional right alternative and semi-alternative algebras are given. As corollaries, we have the algebraic and geometric classification of complex 3-dimensional <span><math><mi>perm</mi></math></span>, binary <span><math><mi>perm</mi></math></span>, associative, <span><math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-, binary <span><math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-, and assosymmetric algebras. In particular, we proved that the first example of non-associative right alternative algebras appears in dimension 3; the first example of non-associative assosymmetric algebras appears in dimension 3; the first example of non-assosymmetric semi-alternative algebras appears in dimension 4; the first example of binary <span><math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-algebras, which is non-<span><math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-, appears in dimension 4; the first example of right alternative algebras, which is not binary <span><math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-, appears in dimension 4; the first example of binary <span><math><mi>perm</mi></math></span> non-<span><math><mi>perm</mi></math></span> algebras appears in dimension 4. As a byproduct, we give an easier answer to problem 2.109 from the Dniester Notebook, previously resolved by Shestakov and Arenas.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 792-824"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321295","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":"Existence of polynomial solutions for an extended bilinear equation of Korteweg-de Vries equation","authors":"Guang-Mei Wei ,&nbsp;Yu-Ping Zhang ,&nbsp;Yu-Xin Song","doi":"10.1016/j.jalgebra.2025.10.002","DOIUrl":"10.1016/j.jalgebra.2025.10.002","url":null,"abstract":"<div><div>In this paper, we investigate the properties of polynomial solutions to an extended bilinear equation of Korteweg-de Vries (KdV) equation by means of differential field and algebraic extension, and prove that the degrees of its polynomial solutions are less than 5, then all rational solutions for the KdV-like equation are provided. Furthermore we point out that some obtained properties can be extended to other bilinear equations and can simplify the computation of finding rational solutions of KdV equation family. With symbolic computation, the four classes nontrivial rational solutions to KdV equation are presented.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 363-373"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334821","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":"Reductions and cores of ideals in polynomial rings over integral domains","authors":"S. Kabbaj ,&nbsp;A. Mimouni ,&nbsp;B. Olberding","doi":"10.1016/j.jalgebra.2025.09.035","DOIUrl":"10.1016/j.jalgebra.2025.09.035","url":null,"abstract":"<div><div>This paper examines reductions and cores of ideals in polynomial rings over integral domains, with a particular focus on valuation and Prüfer domains. The main objective is to derive explicit formulas for reductions and cores of key ideal classes, such as extended ideals, uppers of prime ideals, and divisorial ideals, emphasizing stability and the basic property. To provide a broader foundation, we first examine reductions and cores in extensions of Prüfer domains, establishing key properties of reductions in extensions that are significant on their own and essential for later sections on polynomial rings. By leveraging results on extensions, we further refine explicit computations of the core in polynomial rings and develop new insights into the structure of ideals in these settings. Throughout the paper, illustrative and original examples reinforce the results and clarify the scope of the underlying assumptions.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 59-76"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334822","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 central Nullstellensatz over centrally algebraically closed division rings","authors":"Masood Aryapoor","doi":"10.1016/j.jalgebra.2025.09.033","DOIUrl":"10.1016/j.jalgebra.2025.09.033","url":null,"abstract":"<div><div>We introduce the concept of centrally algebraically closed division rings and show that a division ring satisfies the central Nullstellensatz if and only if it is centrally algebraically closed. We also show that every division ring can be embedded in a centrally algebraically closed division ring.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 377-392"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334830","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":"Cross-positive linear maps, positive polynomials and sums of squares","authors":"Igor Klep ,&nbsp;Klemen Šivic ,&nbsp;Aljaž Zalar","doi":"10.1016/j.jalgebra.2025.09.018","DOIUrl":"10.1016/j.jalgebra.2025.09.018","url":null,"abstract":"<div><div>A ⁎-linear map Φ between matrix spaces is cross-positive if it is positive on orthogonal pairs <span><math><mo>(</mo><mi>U</mi><mo>,</mo><mi>V</mi><mo>)</mo></math></span> of positive semidefinite matrices in the sense that <span><math><mo>〈</mo><mi>U</mi><mo>,</mo><mi>V</mi><mo>〉</mo><mo>:</mo><mo>=</mo><mi>tr</mi><mo>(</mo><mi>U</mi><mi>V</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span> implies <span><math><mo>〈</mo><mi>Φ</mi><mo>(</mo><mi>U</mi><mo>)</mo><mo>,</mo><mi>V</mi><mo>〉</mo><mo>≥</mo><mn>0</mn></math></span>, and is completely cross-positive if all its ampliations <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>⊗</mo><mi>Φ</mi></math></span> are cross-positive. (Completely) cross-positive maps arise in the theory of operator semigroups, where they are sometimes called exponentially-positive maps, and are also important in the theory of affine processes on symmetric cones in mathematical finance.</div><div>To each Φ as above a bihomogeneous form is associated by <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>Φ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>y</mi></mrow><mrow><mi>T</mi></mrow></msup><mi>Φ</mi><mo>(</mo><mi>x</mi><msup><mrow><mi>x</mi></mrow><mrow><mi>T</mi></mrow></msup><mo>)</mo><mi>y</mi></math></span>. Then Φ is cross-positive if and only if <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>Φ</mi></mrow></msub></math></span> is nonnegative on the variety of pairs of orthogonal vectors <span><math><mo>{</mo><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>|</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>T</mi></mrow></msup><mi>y</mi><mo>=</mo><mn>0</mn><mo>}</mo></math></span>. Moreover, Φ is shown to be completely cross-positive if and only if <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>Φ</mi></mrow></msub></math></span> is a sum of squares modulo the principal ideal <span><math><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>T</mi></mrow></msup><mi>y</mi><mo>)</mo></math></span>. These observations bring the study of cross-positive maps into the powerful setting of real algebraic geometry. Here this interplay is exploited to prove quantitative bounds on the fraction of cross-positive maps that are completely cross-positive. Detailed results about cross-positive maps Φ mapping between <span><math><mn>3</mn><mo>×</mo><mn>3</mn></math></span> matrices are given. Finally, an algorithm to produce cross-positive maps that are not completely cross-positive is presented.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 189-243"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334829","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":"Combinatorial density of the set of finitely maximal group actions of prime order on closed oriented surfaces","authors":"Grzegorz Gromadzki,&nbsp;Jakub Szmelter-Tomczuk","doi":"10.1016/j.jalgebra.2025.09.015","DOIUrl":"10.1016/j.jalgebra.2025.09.015","url":null,"abstract":"<div><div>Suppose <span><math><mi>X</mi><mo>=</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> is a compact orientable surface of genus <span><math><mi>g</mi><mo>≥</mo><mn>2</mn></math></span>. A cyclic group <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> of prime order <em>p</em> of orientation-preserving homeomorphisms of <em>X</em> is called finitely maximal if there is no proper finite supergroup <span><math><mi>G</mi><mo>≤</mo><msup><mrow><mi>Homeo</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo></math></span> containing <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>. Peterson et al. (2017) <span><span>[8]</span></span> showed that if <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> is finitely maximal then the number <em>r</em> of fixed points of <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> is maximal, or equivalently the genus <em>h</em> of <span><math><mi>X</mi><mo>/</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> is minimal. Moreover, they exhibited an infinite sequence of genera within which any given action of <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> on <em>X</em> implies <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> is contained in some finite supergroup and demonstrate for genera outside of this sequence the existence of at least one finitely maximal <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-action. Here we show that the set of equivalence classes of finitely maximal cyclic actions of a fixed Teichmüller dimension <em>d</em> defined as <span><math><mn>3</mn><mo>(</mo><mi>h</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>r</mi></math></span> is combinatorially dense, in a suitable sense, in the set of classes of all actions of prime order of such dimension. This is a bit of a surprising result in the context of the results of Peterson, Russell and Wootton and it has some consequences concerning the singular locus of the moduli space of algebraic curves of a given genus, which we briefly describe at the end of the Introduction.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 77-90"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334831","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}