Abstract

The following Artin theorem about alternative linear algebras defined on the commutative, associative ring with unity is well-known: in an alternative linear algebra, if \((a,b,c)=0\), then the subalgebra generated by the elements \(a\), \(b\), and \(c\) is associative. In this paper a wide generalization of this classical result is proposed using the concepts of hyperidentity and coidentity. The corresponding universal algebras are referred to as \(g\)-algebras.

中文翻译：

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Artin定理的推广

摘要

以下关于在具有单位交换性，缔合环上定义的替代线性代数的Artin定理是众所周知的：在替代线性代数中，如果\（（a，b，c）= 0 \），则元素生成的子代数\（a \），\（b \）和\（c \）是关联的。在本文中，使用超身份和共身份的概念对这一经典结果进行了广泛的概括。对应的通用代数称为\（g \）-代数。