Semigroups generated by partitions

Abstract

Let $X$ be a nonempty set and $X^2$ be the Cartesian square of $X$. Some semigroups of binary relations generated partitions of $X^2$ are studied. In particular, the algebraic structure of semigroups generated by the finest partition of $X^2$ and, respectively, by the finest symmetric partition of $X^2$ are described.

47 pages, 5 figures