分式半环及性质

Fractional Semiring and Properties

首先在交换半环与其乘法集合的卡氏积上定义了一种等价关系,从而构造了一类新的交换半环.即公式半环.讨论了交换半环与其分式半环之间的关系,然后刻划分式半环的泛性质.最后,在两个可换可消半群的直积上定义相同的关系,证得该关系为群同余,得到相近的结果.

In this paper,we first defined a kind of equiva lence relation on the cartersian product of commutative semiring and multiplicative set, furthermore, we structured a new kind of commutative semiring, namely fractional semiring. We discussed the relation between commutative semiring and fractional semiring, then we characterized the universal property of fractional semiring. In the end, we defined the same relation on the direct prooduct of two commutative cancellable semigroups,then proved this relation is group commgruence. A similar result is found.