Nonmatrix Varieties of Nonassociative Algebras

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-12-23 DOI:10.1007/s10469-024-09763-0

I. P. Shestakov, V. S. Bittencourt

引用次数: 0

Abstract

A variety of associative algebras is nonmatrix if it does not contain the algebra of 2 × 2 matrices over a given field. Nonmatrix varieties were introduced and studied by V. N. Latyshev in [Algebra and Logic, 16, No. 2, 98-122 (1977); Algebra and Logic, 16, No. 2, 122-133 (1977); Mat. Zam., 27, No. 1, 147-156 (1980)] in connection with the Specht problem. A series of equivalent characterizations of nonmatrix varieties was obtained in [Isr. J. Math., 181, No. 1, 337-348 (2011)]. In the present paper, the notion of nonmatrix variety is extended to nonassociative algebras, and their characterization from the last-mentioned paper is generalized to alternative, Jordan, and some other varieties of algebras.

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非结合代数的非矩阵变异

如果在给定的域上不包含2 × 2矩阵的代数，那么这个组合代数就是非矩阵。V. N. Latyshev在[代数与逻辑，16,No. 2], 98-122（1977）中引入并研究了非矩阵变分；《代数与逻辑》，16,No. 2, 122-133 (1977)；垫,祖阿曼。， 27, No. 1, 147-156(1980)]与Specht问题有关。在[Isr]中得到了一系列非矩阵变量的等价表征。j .数学。生态学报，181,No. 1, 337-348（2011）。本文将非矩阵变异的概念推广到非结合代数，并将非结合代数的性质推广到alternative、Jordan和其他代数的变异。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.