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In this paper, we introduce and study V- and CI-semirings---semirings all ofwhose simple and cyclic, respectively, semimodules are injective. We describeV-semirings for some classes of semirings and establish some fundamentalproperties of V-semirings. We show that all Jacobson-semisimple V-semirings areV-rings. We also completely describe the bounded distributive lattices,Gelfand, subtractive, semisimple, and anti-bounded, semirings that areCI-semirings. Applying these results, we give complete characterizations ofcongruence-simple subtractive and congruence-simple anti-bounded CI-semiringswhich solve two earlier open problems for these classes of CI-semirings.

On V-Semirings and Semirings all of whose Cyclic Semimodules are Injective