V-semirings

Abstract

We investigate the semirings over which all simple semimodules are injective. In ring and module theory, the rings with an analogous condition are called V-rings. Therefore it is natural to call the semirings under consideration V-semirings. We obtain the semiring analogs of some well-known results on V-rings, including an analog of Kaplansky's theorem on commutative V-rings. © 2012 Pleiades Publishing, Ltd.