h-半正则子半环与模糊h-半正则子半环

h-hemiregular Subhemiring and Fuzzy h-hemiregular Subhemiring

通过在半环上引入元素的h-半正则子集,给出h-半正则子半环和模糊h-半正则子半环的定义,利用模糊子集的水平截集讨论了两个概念之间的关系.证明了h-半正则子半环(模糊h-半正则子半环)在同态满射下的象还是h-半正则子半环(模糊h-半正则子半环),而在同构映射下的逆象仍为h-半正则子半环(模糊h-半正则子半环).最后给出了h-半正则子半环和模糊h-半正则子半环的等价刻划.

The concepts of h-hemiregular subhemiring and fuzzy h-hemiregular subhemiring are introduced by the h-hemiregular subset of the elements in a hemiring, and the relationship between the two concepts is dis- cussed, It is proved that the image of a h-hemiregular subhemiring （ fuzzy h-hemiregular subhemiring） under an epimorphism is also a h-hemiregular subhemiring （fuzzy h-hemiregular subhemiring） and the inverse image of a h-hemiregular subhemiring （fuzzy h-hemiregular subhemiring） under an isormorphsm is still a h-hemireg- ular subhemiring （fuzzy h-hemiregular subhemiring）. Finally,the equivalent conditions for h-hemiregular sub- hemiring and fuzzy h-hemiregular hemiring are given.