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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Last modified: April 11, 2000