Geodesic
$\mathbf U$-semigroups of relations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 51-61.

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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. 
@article{FPM_2000_6_1_a4,
     author = {D. A. Bredikhin},
     title = {$\mathbf U$-semigroups of relations},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {51--61},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a4/}
}
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D. A. Bredikhin. $\mathbf U$-semigroups of relations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 51-61. http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a4/