基于可减的实半环与实素理想

Real semiring based on being subtractive and real prime ideals

半环R被称为实半环,若对于任意的n∈N,方程x12+…+xn2=0在R中只有零解:x1=…=xn=0.为了刻画实半环,引入了实理想和极小素理想的概念,利用同余的方法,得到了可减半环类中实半环的结构定理.

A semiring R is called a real semiring if an equation that x1^2＋…＋xn^2 = 0 only has zero solutions in R： x1 =…= xn = 0.In order to describe the real semings,the methods of congruences are used,the conceptions of real ideals and minimal prime ideals are introduced in the paper.The structure theorems of real semirings in the class of the subtractive semirings are obtained.