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 ${\mathbf{M}}_n(S)$, of all $n\times n$ matrices over a semiring $S$, is congruence-simple, provided that either $S$ has a multiplicatively absorbing element or $S$ is commutative and additively cancellative.

11 pages

References in corpus (3)

• Simpleness of Leavitt Path Algebras with Coefficients in a Commutative Semiring
• On congruence-semisimple semirings and the $K_0$-group characterization of ultramatricial algebras over semifields
• Idempotence of finitely generated commutative semifields