有限生成替代代数的斜对称同一性

IF 0.4 3区数学 Q4 LOGIC Algebra and Logic Pub Date : 2024-04-18 DOI:10.1007/s10469-024-09740-7

I. P. Shestakov

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引用次数: 0

摘要

我们证明，对于每一个自然数 n，都存在一个自然数 N (n)，使得在 N (n) 或更多变量中消失的每一个多线性偏斜对称多项式，在自由关联代数中消失，也在特征为 0 的域上任何 n 生成的替代代数中消失。在此之前，只有 I. P. 谢斯塔科夫在[《代数与逻辑》，16，第 2 期，153-166（1977 年）]中构建的一系列倾斜对称多项式证明了类似的结果。

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Skew-Symmetric Identities of Finitely Generated Alternative Algebras

We prove that for every natural number n, there exists a natural number N (n) such that every multilinear skew-symmetric polynomial in N (n) or more variables which vanishes in the free associative algebra also vanishes in any n-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, 16, No. 2, 153-166 (1977)].

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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.

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