FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 51-61

U-semigroups of relations

D. A. Bredikhin

Abstract

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By a u-semigroup we mean an algebra (A,×,u) where (A,×) is a semigroup and u Î A. A set of binary relations closed under the relation product and containing the universal relation U forms a U-semigroup of relations which can be considered as partially ordered by inclusion. In the paper, an axiomatic description of the classes of U-semigroups and partially ordered U-semigroups of relations, and a basis of identities and quasiidentities of the variety and quasivariety generated by these classes are obtained.


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