Algebras defined by equations

JOURNAL OF ALGEBRA

卷:555

Article

Higgins, Peter M.¹  Jackson, Marcel² 

[1] Univ Essex, Dept Math Sci, Colchester, Essex, England

[2] La Trobe Univ, Dept Math & Stat, Bundoora, Vic 3086, Australia

关键词: Equational classes;    Regular semigroups;    Model theory;   

DOI  :  10.1016/j.jalgebra.2020.01.029

来源: Elsevier

【 摘 要 】

We show that an elementary class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular semigroups this allows an interpretation of a universal algebraic nature that is formulated entirely in terms of the associative binary operation of the semigroup, which serves as an alternative to the approach via so called e-varieties. In particular we prove that classes of Inverse semigroups, Orthodox semigroups, and E-solid semigroups are equational in our sense. We also examine which equations are valid in every semigroup. Crown Copyright (C) 2020 Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free