Classification of Dual Distributive Hyperidentities in Divisible Algebras

Pub Date : 2024-08-09 DOI:10.3103/s1068362324700225

Yu. M. Movsisyan, S. S. Davidov

引用次数: 0

Abstract

The paper provides a classification of nontrivial dual hyperidentities of the left and right distributivity satisfied in functionally nontrivial divisible algebras. If the nontrivial dual hyperidentities of the left and right distributivity hold in a functionally nontrivial divisible algebra, then the hyperidentity of the left distributivity is of rank two and is (equivalent to the hyperidentity) of the form

$$X(x,Y(y,z))=Y(X(x,y),X(x,z)),$$

while the hyperidentity of the right distributivity is the hyperidentity of rank two and is (equivalent to the hyperidentity) of the form

$$X(Y(x,y),z)=Y(X(x,z),X(y,z)).$$

For the classification of nontrivial hyperidentities of the left and right distributivity satisfying in functionally nontrivial $q$-algebras, see [1–4].

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可分代数中双重分配超同性的分类

摘要本文对函数非琐碎可分代数中满足的左分配性和右分配性的非琐碎对偶超同一性进行了分类。如果在函数非三维可分代数中，左分配性和右分配性的非琐对偶超同一性成立，那么左分配性的超同一性是秩二的（等价于超同一性），其形式为$$X(x. Y(y,z))=Y(x. Y(y,z))、Y(y,z))=Y(X(x,y),X(x,z))$$而右分配性的超同一性是秩为二的超同一性，其形式为$X(Y(x,y),z)=Y(X(x,z),X(y,z))（等价于超同一性）。$$关于在函数非三维 $q$-algebras 中满足左分配性和右分配性的非三维超同一性的分类，请参见[1-4].

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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