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On using the join operation to define classes of algebras

Vernitski, A (2008) 'On using the join operation to define classes of algebras.' Communications in Algebra, 36 (3). 1088 - 1096. ISSN 0092-7872

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Abstract

We call a class of algebras a finitary prevariety if the class is closed under the formation of subalgebras and finitary direct products, and contains the one-element algebra. The join of two finitary prevarieties and a concept of a join-irreducible finitary prevariety may be introduced naturally. We develop techniques for proving that a finitary prevariety of semigroups is join-irreducible, and find many examples of join-irreducible finitary prevarieties of semigroups. For example, we prove that if a class of finite semigroups is defined by ω-identities and contains the class J, then it is a join-irreducible finitary prevariety. Copyright © Taylor & Francis Group, LLC.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 04 Jan 2012 11:21
Last Modified: 30 Jan 2019 16:16
URI: http://repository.essex.ac.uk/id/eprint/1805

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