We prove that if the direct sum of a family of semimodules over a semiring S is an injective semimodule or if the direct product of a family of semimodules over S is a projective semimodule, then the cardinality of the ...

© 2016 World Scientific Publishing Company.As is well-known, every module over a ring has an injective envelope; however, that fact does not hold, in general, for semimodules over semirings. We study the problem of existence ...

Among other results of this paper, we single out the following ones. We show that division rings are the only division semirings over which the categories of semimodules are Schreier varieties, i.e., all subsemimodules of ...

Necessary and sufficient conditions for the regularity of complete matrix semirings over au arbitrary semiring are obtained. ©2001 Plenum Publishing Corporation.

© 2016 Elsevier Inc.In this paper, we introduce homological structure theory of semirings and CP-semirings — semirings all of whose cyclic semimodules are projective. We completely describe semisimple, Gelfand, subtractive, ...