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Algebras defined by equations

Higgins, Peter and Jackson, Marcel (2020) 'Algebras defined by equations.' Journal of Algebra, 555. ISSN 0021-8693

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: Equational classes, Regular semigroups, Model theory
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 24 Mar 2020 11:13
Last Modified: 01 May 2020 11:15
URI: http://repository.essex.ac.uk/id/eprint/27159

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