乘法半群(S,·)为矩形群的双半环  

Bi-semirings whose multiplicative semigroup(S,·) is rectangular group

作　　者：刘立[1] 李刚[1] LIU Li LI Gang(Institute of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

机构地区：[1]山东师范大学数学与统计学院,山东济南250014

出　　处：《山东科学》2017年第1期89-94,共6页Shandong Science

摘　　要：本文研究了(S,+)半群为半格、(S,·)半群为矩形群、(S,*)半群为半格的双半环。从双半环的两个子集出发构造两个偏序关系,得到了双半环的(S,·)半群上的Green-■关系■是双半环同余的一个充要条件,并给出了■是双半环同余的等价命题。The bi-semirings whose semigroups （S, ·） are semilattices, semigroups （S, · ） are rectangular groups and semigroups （ S, · ） are semilattices were studied in this paper. Two partial order relations were constructed on two subsets of a bi-semiring, and a necessary and sufficient condition for that the Green-H relation on semigroups （S, · ） is a bisemiring congruence was obtained. Furthermore, the equivalent proposition that is a bi-semiring congruence was presented.

关 键 词：半格 双半环 矩形群 偏序 同余 

分 类 号：O152.7[理学—数学]