On Tensor Product Semirings

Abstract

In this paper we study tensor product semirings of the form [Formula: see text], where [Formula: see text] are [Formula: see text]-semimodules for a semiring [Formula: see text] and [Formula: see text] is a bilinear map. We establish connections between tensor product semirings and Morita equivalence of semirings with identity. Under a pseudo-surjectivity condition on [Formula: see text], we prove that quotient of a tensor product semiring by its congruence is again tensor product semiring constructed from appropriate quotient semimodules and quotient semiring. Finally, we explore certain relations between tensor product semirings and Rees matrix semirings.