一类幂等半环对分配格的刻画  

Distributive Lattice Characterized by a Class of Idempotent Semirings

作　　者：朱天民[1] 

机构地区：[1]渭南师范学院数学与应用数学研究所,陕西渭南714100

出　　处：《青岛科技大学学报（自然科学版）》2007年第2期178-179,188,共3页Journal of Qingdao University of Science and Technology:Natural Science Edition

基　　金：陕西省自然科学研究基金项目(2003A10);陕西省教育厅自然科学专项基金项目(06JK302)

摘　　要：研究了一类可表示为分配格的幂等半环,即加法半群为半格的乘法带半环;通过Green-D关系,得到了加法群为半格的乘法带半环的若干性质;证明了如果半环S的加法半群是半格,则S是乘法带半环当且仅当S是分配格;从而获得分配格结构的一种刻画。A class of idempotent semirings which can be showed distributive lattice,i, e. , multiplicative band semirings which additive reducts are semilattice are studied in this paper . Some properties of multiplicative bond semirings are obtained by Green-D relation. We also proved S∈S,S is multiplicative band semirings if and only if S is distributive lattice. The characterization for structure of distributive lattice is obtained.

关 键 词：乘法带半环 加法半格 分配格 

分 类 号：O153[理学—数学]