Congruence-simple matrix semirings

Abstract

It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring [Formula: see text], of all [Formula: see text] matrices over a semiring [Formula: see text], is congruence-simple, provided that either [Formula: see text] has a multiplicatively absorbing element or [Formula: see text] is commutative and additively cancellative.