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Skew-Symmetric Identities of Finitely Generated Alternative Algebras 有限生成替代代数的斜对称同一性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-04-18 DOI: 10.1007/s10469-024-09740-7
I. P. Shestakov
{"title":"Skew-Symmetric Identities of Finitely Generated Alternative Algebras","authors":"I. P. Shestakov","doi":"10.1007/s10469-024-09740-7","DOIUrl":"10.1007/s10469-024-09740-7","url":null,"abstract":"<p>We prove that for every natural number n, there exists a natural number <i>N</i> (<i>n</i>) such that every multilinear skew-symmetric polynomial in <i>N</i> (<i>n</i>) or more variables which vanishes in the free associative algebra also vanishes in any <i>n</i>-generated alternative algebra over a field of characteristic 0. Previously, a similar result was proved only for a series of skew-symmetric polynomials constructed by I. P. Shestakov in [Algebra and Logic, <b>16</b>, No. 2, 153-166 (1977)].</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 3","pages":"257 - 265"},"PeriodicalIF":0.4,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140612565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Axiomatizability of the Class of Subdirectly Irreducible S-Acts over a Commutative Monoid 交换单元上的次直接不可还原 S 作用类的可公理化性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-02-16 DOI: 10.1007/s10469-024-09735-4
A. A. Stepanova, E. L. Efremov
{"title":"Axiomatizability of the Class of Subdirectly Irreducible S-Acts over a Commutative Monoid","authors":"A. A. Stepanova,&nbsp;E. L. Efremov","doi":"10.1007/s10469-024-09735-4","DOIUrl":"10.1007/s10469-024-09735-4","url":null,"abstract":"<p>An axiomatizability criterion is found for the class of subdirectly irreducible <i>S</i>-acts over a commutative monoid. As a corollary, a number of properties are presented which a commutative monoid should satisfy provided that the class of subdirectly irreducible acts over it is axiomatizable. The question about a complete description of monoids over which the class of subdirectly irreducible acts is axiomatizable remains open even for the case of a commutative monoid.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 2","pages":"179 - 200"},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Varieties of Exponential R-Groups 指数 R 群的变种
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-02-15 DOI: 10.1007/s10469-024-09731-8
M. G. Amaglobeli, A. G. Myasnikov, T. T. Nadiradze
{"title":"Varieties of Exponential R-Groups","authors":"M. G. Amaglobeli,&nbsp;A. G. Myasnikov,&nbsp;T. T. Nadiradze","doi":"10.1007/s10469-024-09731-8","DOIUrl":"10.1007/s10469-024-09731-8","url":null,"abstract":"<p>The notion of an exponential <i>R</i>-group, where <i>R</i> is an arbitrary associative ring with unity, was introduced by R. Lyndon. Myasnikov and Remeslennikov refined the notion of an <i>R</i>-group by introducing an additional axiom. In particular, the new concept of an exponential <i>MR</i>-group (<i>R</i>-ring) is a direct generalization of the concept of an <i>R</i>-module to the case of noncommutative groups. We come up with the notions of a variety of <i>MR</i>-groups and of tensor completions of groups in varieties. Abelian varieties of <i>MR</i>-groups are described, and various definitions of nilpotency in this category are compared. It turns out that the completion of a 2-step nilpotent <i>MR</i>-group is 2-step nilpotent.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 2","pages":"119 - 136"},"PeriodicalIF":0.4,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An Explicit Basis for WCP-Globally Admissible Inference Rules WCP 全球可接受推理规则的明确基础
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-02-15 DOI: 10.1007/s10469-024-09733-6
V. V. Rimatskii
{"title":"An Explicit Basis for WCP-Globally Admissible Inference Rules","authors":"V. V. Rimatskii","doi":"10.1007/s10469-024-09733-6","DOIUrl":"10.1007/s10469-024-09733-6","url":null,"abstract":"<p>Inference rules are examined which are admissible immediately in all residually finite extensions of <i>S</i>4 possessing the weak cocover property. An explicit basis is found for such <i>WCP</i>-globally admissible rules. In case of tabular logics, the basis is finite, and for residually finite extensions, the independency of an explicit basis is proved.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 2","pages":"148 - 165"},"PeriodicalIF":0.4,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Horizontal Joinability on 5-Dimensional 2-Step Carnot Groups with a Codimension 2 Horizontal Distribution 具有同维度 2 水平分布的 5 维 2 步卡诺群的水平可接性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-02-15 DOI: 10.1007/s10469-024-09732-7
R. I. Zhukov, A. V. Greshnov
{"title":"Horizontal Joinability on 5-Dimensional 2-Step Carnot Groups with a Codimension 2 Horizontal Distribution","authors":"R. I. Zhukov,&nbsp;A. V. Greshnov","doi":"10.1007/s10469-024-09732-7","DOIUrl":"10.1007/s10469-024-09732-7","url":null,"abstract":"<p>For a 5-dimensional 2-step Carnot group <i>G</i><sub>3,2</sub> with a codimension 2 horizontal distribution, we prove that any two points <i>u</i>, <i>v</i> ∈ <i>G</i><sub>3,2</sub> can be joined on it by a horizontal broken line consisting of at most three segments. A multi-dimensional generalization of this result is given.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 2","pages":"137 - 147"},"PeriodicalIF":0.4,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Generalized Schur Groups 广义舒尔群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-02-14 DOI: 10.1007/s10469-024-09734-5
G. K. Ryabov
{"title":"Generalized Schur Groups","authors":"G. K. Ryabov","doi":"10.1007/s10469-024-09734-5","DOIUrl":"10.1007/s10469-024-09734-5","url":null,"abstract":"<p>An <i>S</i>-ring (Schur ring) is said to be central if it is contained in the center of a group ring. We introduce the notion of a generalized Schur group, i.e., a finite group such that all central <i>S</i>-rings over this group are Schurian. It generalizes the notion of a Schur group in a natural way, and for Abelian groups, the two notions are equivalent. We prove basic properties and present infinite families of non-Abelian generalized Schur groups.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 2","pages":"166 - 178"},"PeriodicalIF":0.4,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Complexity of Inversion in Groups 群体反转的复杂性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-02-13 DOI: 10.1007/s10469-024-09730-9
P. E. Alaev
{"title":"The Complexity of Inversion in Groups","authors":"P. E. Alaev","doi":"10.1007/s10469-024-09730-9","DOIUrl":"10.1007/s10469-024-09730-9","url":null,"abstract":"<p>We prove that if <span>(mathcal{A})</span> = (<i>A</i>,⋅) is a group computable in polynomial time (P-computable), then there exists a P-computable group <span>(mathcal{B})</span> = (<i>B</i>,∙) ≅ <span>(mathcal{A},)</span> in which the operation <i>x</i><sup>−1</sup> is also <i>P-</i>computable. On the other hand, we show that if the center <span>(Zleft(mathcal{A}right))</span> of a group A contains an element of infinite order, then under some additional assumptions, there exists a P-computable group <span>({mathcal{B}}{prime}=left({B}{prime},cdot right)cong mathcal{A})</span> in which the operation <i>x</i><sup><i>−</i>1</sup> is not primitive recursive. Also the following general fact in the theory of P-computable structures is stated: if <span>(mathcal{A})</span> is a P-computable structure and <i>E</i> ⊆ <i>A</i><sup>2</sup> is a P-computable congruence on <span>(mathcal{A},)</span> then the quotient structure <span>(mathcal{A}/E)</span> is isomorphic to a P-computable structure.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 2","pages":"103 - 118"},"PeriodicalIF":0.4,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Letter to the Editorial Board 致编辑委员会的信
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-02-09 DOI: 10.1007/s10469-024-09736-3
Yu. L. Ershov
{"title":"Letter to the Editorial Board","authors":"Yu. L. Ershov","doi":"10.1007/s10469-024-09736-3","DOIUrl":"10.1007/s10469-024-09736-3","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 2","pages":"201 - 201"},"PeriodicalIF":0.4,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139849470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Sessions of the Seminar “Algebra i Logika” 代数与逻辑 "研讨会课程
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-02-09 DOI: 10.1007/s10469-024-09737-2
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-024-09737-2","DOIUrl":"10.1007/s10469-024-09737-2","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 2","pages":"202 - 202"},"PeriodicalIF":0.4,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139847928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Splitting of Normalizers of Maximal Tori in Finite Groups of Lie Type 列型有限群中最大环的归一化分裂
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-01-05 DOI: 10.1007/s10469-023-09721-2
A. A. Galt, A. M. Staroletov
{"title":"Splitting of Normalizers of Maximal Tori in Finite Groups of Lie Type","authors":"A. A. Galt,&nbsp;A. M. Staroletov","doi":"10.1007/s10469-023-09721-2","DOIUrl":"10.1007/s10469-023-09721-2","url":null,"abstract":"<p>Let <i>G</i> be a finite group of Lie type, and <i>T</i> some maximal torus of the group <i>G</i>. We bring to a close the study of the question of whether there exists a complement for a torus <i>T</i> in its algebraic normalizer <i>N</i> (<i>G, T</i>). It is proved that any maximal torus of a group <i>G</i> ∈ {<i>G</i><sub>2</sub>(<i>q</i>), <sup>2</sup><i>G</i><sub>2</sub>(<i>q</i>), <sup>3</sup><i>D</i><sub>4</sub>(<i>q</i>)} has a complement in its algebraic normalizer. Also we consider the remaining twisted classical groups <sup>2</sup><i>A</i><sub><i>n</i></sub>(<i>q</i>) and <sup>2</sup><i>D</i><sub><i>n</i></sub>(<i>q</i>).</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"22 - 40"},"PeriodicalIF":0.4,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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