乘法半群为逆半群的半环  

Semirings whose multiplicative reduct is inverse semigroup

作　　者：邵勇[1] 赵宪钟[1] 潘秀娟[1] 

机构地区：[1]西北大学数学系,陕西西安710069

出　　处：《西北大学学报（自然科学版）》2006年第3期345-347,共3页Journal of Northwest University（Natural Science Edition）

基　　金：陕西省自然科学研究基金资助项目(2003A10);陕西省教育厅自然科学专项基金资助项目(02JK053)

摘　　要：目的求证加法导出是半格、乘法导出是逆半群的半环成为分配格的充要条件。方法加法半群和乘法半群上的偏序以及二者之间的关系。结果给出了该类半环成为分配格的几个等价命题。结论推广了双半格成为分配格的一些结果。Aim In order to prove a semiring whose additive reduct is a semilattice and multiplicative reduct is a inverse semigroup to be a distributive lattice. Methods Using partial orders on multiplicative reduct and additive reduct and relations between two partial orders. Results Some equivalent statements are obtained concerning a semiring becoming a distributive lattice. Conclusion Some known results about bi-semilattice becoming distributive lattice are expanded.

关 键 词：半群 半环 半格 分配格 偏序关系 

分 类 号：O152.7[理学—数学]