半环的强理想与素半环

本文引入半环强理想的概念,证明了这种半环的强理想与同余是互相唯一决定的,从而利用理想作商是可行的.据此,建立了素半环、半素半环的概念,并且讨论了它们的一代数性质.

The Strong Ideal of Semiring and Prime-semiring

In this paper,we introduced the concept of the strong ideal in a semiring whose additional semirings are groups,the ideal of a semiring in the class and its congruenee are the only determinant to each other.So,it is feasible to make quotient by ideal of a semir- ing.On basis of it,the concepts of prime-semirngs and semiprime-semirings are established and some algebraic properties of theirs are discussed in the paper.