A Generalization of the Jacobson-Chevalley Density Theorem

Abstract:

      In this paper the structure of a completely primitive hemiring is studied. In the meanwhile the Jacobson-Chevalley density theorem is generalized. At first it is shown that a right R-semimodule M (R is a hemiring) is enbedded in an R-se-mimodule M, which is a group relative to addition. Next a semi-linearly independent set (over S) in a S-semimodule is defined. Let R be a S-endomorphism semiring of a left S-semimodule M. of course M is a right R-semimodule and so is M.