中文摘要：

在交换半环范畴中引进＂半实理想＂,＂实理想＂和＂凸理想＂等概念,从而将实代数学中有关（半）实环的主要结果推广到交换半环上。如下两个结果被建立：（1）一个半环是半实的,当且仅当它有一个实素理想;（2）半环中一个理想为实的,当且仅当它是若干个实素理想的交集。

英文摘要：

The notions of real ideals,semireal ideals and convex ideals are introduced in the category of commutative semirings,and some important results on real or semireal rings are generalized to commutative semirings.Two such results are established：（1） A commutative semiring is semireal,if and only if it possesses a real prime ideal;（2） An ideal of a semiring is real,if and only if it is an intersection of real prime ideals.