Jacobson-Chevalley稠密定理的一个推广

我们在1]中证明了,一个半环(hemiring)关于它的Jacobson关系根的商同构于完全本原半环的亚直和。这使我们有兴趣对这个特殊的半环类——完全本原半环的结构作进一步的讨论。本文的主要结果是:一个半环是完全本原的当且仅当它是一个半模上的亚稠密自同态半环。这个定理给出了完全本原半环的结构,推广了Jacobson—Chevalley稠密定理。

A Generalization of the Jacobson-Chevalley Density Theorem

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.