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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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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

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