中文摘要：

在交换半环范畴中引进和研究理想的实根，从而将实代数学中有关结果推广到交换半环上。如下结果被建立：在半环中，一个理想的实根恰等于包含该理想的所有实理想的交集，并也恰等于包含该理想的所有实素理想的交集。此外，形式更为一般的理想的实根--广义实根被考虑，并获得相应的结果。

英文摘要：

The notion of real radicals of ideals was introduced in the category of commutative semirings. Similar to the category of commutative rings,the following resultwere established： The real radical of an ideal in a commutative semiring was the intersection of real ideals,with this ideal being inclusive,and also was the intersection of real prime ideals containing this one. Moreover,a kind of generalized real radicals of ideals was investigated too in the category of commutative semirings,and the corresponding result was obtained.