乘法半群为左正规纯正群的半环  

Semirings for which multiplicative reducts are left normal orthogroups

作　　者：杨琳[1] 邵勇[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《纯粹数学与应用数学》2010年第1期146-150,共5页Pure and Applied Mathematics

基　　金：国家自然科学基金(10471112);陕西省教育厅自然科学专项基金(07JK413);西北大学科学研究基金(09nw-25)

摘　　要：研究了加法半群为半格,乘法半群为左正规纯正群的半环.证明了此类半环(S,+,·)可以嵌入到半格(S,+)的自同态半环中.构造S的一个特定的偏序关系,得到了(S,·)上的自然偏序与所构造偏序相等的等价条件.In this paper, the semirings for which additive reducts are semilattices and multiplicative reducts are left normal orthogroups are studied. That semiring （S, ＋, .） is embedded into the endomorphism semiring of the semilattice （S, ＋） is proved. The partial order relation on semiring S is constructed and the equivalent condition in order to the natural order on multiplicative reduct of semiring S is equivalent to the constructed partial order on semiring S is obtained.

关 键 词：半群 半环 左正规纯正群 半格 偏序关系 

分 类 号：O152.7[理学—数学]