弱左C-rpp半群  

On Weakly Left C-rpp Semigroups

作　　者：袁莹[1] 任学明[1] 宫春梅[1] YUAN Ying;REN Xueming;GONG Chunmei(College of Science,Xi'an University of Architecture and Technology,Xi'an,Shaanxi,710055,P.R.China)

机构地区：[1]西安建筑科技大学理学院,西安陕西710055

出　　处：《数学进展》2021年第4期561-570,共10页Advances in Mathematics（China）

基　　金：supported by Special Research Foundation of Education Department of Shaanxi Province(No.18JK0442);Research Foundation of Xi’an University of Architecture and Technology(No.ZR18035);supported by NSFC(No.12001418)。

摘　　要：本文研究一类弱rpp半群,即所谓弱左C-rpp半群.在该类半群半格分解基础上证明了每一个弱左C-rpp半群均可表示为一个幂零幺半群的强半格与一个左正则带的左交叉积.该结果是[Semigroup Forum,1976/77,13(3):229-237]中关于C-rpp半群及[Semigroup Forum,1995,50(1):9-23]中关于左C-rpp半群结论的一个共同推广.A kind of weakly rpp semigroups,namely,weakly left C-rpp semigroups,is studied.After giving a semilattice decompositions of weakly left C-rpp semigroups,we prove that every weakly left C-rpp semigroup can be expressed as a left cross product of a strong semilattice of unipotent monoids and a left regular band.These work may be regarded as extending the results in[Semigroup Forum,1976/77,13(3):229-237]for C-rpp semigroups and in[Semigroup Forum,1995,50(1):9-23] for left C-rpp semigroups.

关 键 词：RPP半群 弱rpp半群 弱左C-rpp半群 左交叉积 

分 类 号：O152.7[理学—数学]