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arXiv · 1810.13012

Algebras defined by equations

Peter M Higgins·Marcel Jackson
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Abstract

We show that a 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 in particular 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.

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Peter M Higgins, Marcel Jackson. 2019-12-20. Algebras defined by equations. https://doi.org/10.1016/j.jalgebra.2020.01.029

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