Some constructions related to Rees matrix semigroups

Abstract

For the translational hulls of two Rees matrix semigroups represented by means of matrices, we construct all their isomorphisms again in matrix form. These are matrices of arbitrary size over a group with zero satisfying certain conditions on nonzero entries. We introduce the concept of a r-maximal completely 0-simple and of a Rees matrix semigroup. To this end, we construct a Rees matrix semigroup from a group and a nonempty set and introduce the concept of a column tight Rees matrix semigroup. We study these concepts in relation to the translational hull of a Rees matrix semigroup.