Split Quasi-adequate Semigroups  

作　　者：Xiao Jiang GUO Ting Ting PENG 

机构地区：[1]Department of Mathematics,Jiangxi Normal University,Nanchang 330022,P.R.China [2]Department of Base,Jiangxi V&T College of Communication,Nanchang 330013,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2012年第2期425-438,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China of China(Grant No.10961014);Natural Science Foundation of Jiangxi Province;the SF of Education Department of Jiangxi Province,China(Grant No.GJJ11388)

摘　　要：The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by McAlister and Blyth on split orthodox semigroups.The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by McAlister and Blyth on split orthodox semigroups.

关 键 词：Quasi-adequate semigroup adequate semigroup adequate transversal regular band type-A semigroup 

分 类 号：O152.7[理学—数学] O657.720.3[理学—基础数学]