The intersection of the maximal regular subsemigroups of the semigroup of binary relations.
We study the structure of the ideals of the semigroup of all isotone (order-preserving) partial injections as well as of the semigroup of all monotone (order-preserving or order-reversing) partial injections on an n-element set. The main result is the characterization of the maximal subsemigroups of the ideals of and .
We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it.
We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it.