FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

D. A. Bredikhin

Abstract

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```
By a
```$\mathbf u$ -semigroup
we mean an algebra $(A,\cdot,\mathbf u)$
where $(A,\cdot)$ is
a semigroup and $\mathbf u \in A$ .
A set of
binary relations closed under the relation product and containing
the universal relation $\mathbf U$
forms a $\mathbf U$ -semigroup of
relations which can be considered as partially ordered by
inclusion. In the paper, an axiomatic description of
the classes of $\mathbf U$ -semigroups and partially ordered
$\mathbf U$ -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