中文摘要：

在有单位元的交换半环上,引入赋值和实赋值的概念,在此基础上建立有关半环上赋值和实赋值的一些基本结论。此外,引入了赋值与亚序之间的相容性,并通过赋值与亚序的相容性建立了一个赋值是实赋值的充分必要条件。

英文摘要：

The notions of valuations and real valuations were introduced in the category of commutative semirings with units.Some basic results on valuations and real valuations of semirings were derived.Moreover,the compatibility between preorderings and valuations was analyzed for a commutative semirings.It also proved that a valuation,as a necessary and sufficient condition,is real if and only if it is compatible with some preordering.