Abstract

In this paper, we consider from two different perspectives the concept of “Morita equivalence” in a (non-additive) semiring setting, as well as its application to homological characterization of semirings. Among other results, we present an analog of the Eilenberg–Watts theorem for module categories in the semimodule setting and give various homological characterizations of semisimple and subtractive semirings. We also solve Problem 3.9 in [Y. Katsov, On flat semimodules over semirings, Algebra Universalis 51 (2004) 287–299] for the class of additively regular semisimple semirings, showing that for semimodules over semirings of this class the concepts of “mono-flatness” and “flatness” coincide.