关于C o-rpp半群与C o-wrpp半群（英文）  

On C o-rpp Semigroups and C o-wrpp Semigroups

作　　者：陈益智[1] 赵宪钟[2] 

机构地区：[1]惠州学院数学系,惠州广东516007 [2]江西师范大学数学与信息科学学院,南昌江西330027

出　　处：《数学进展》2015年第6期827-836,共10页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11501237,No.11401246,No.11426112);the NSF of Fujian Province(No.2014J01019);the NSF of Guangdong Province(No.2014A030310087,No.2014A030310119);the Outstanding Young Teacher Training Program in Guangdong Universities;the Outstanding Young Innovative Talent Training Project in Guangdong Universities(No.2013LYM0086);the Science Technology Project of Huizhou City

摘　　要：本文首先定义了一类真包含C-rpp半群的C o-rpp半群,并证明了半群S是满足L^o(S)是右同余的C o-rPP半群当且仅当它是左o-幺半群的强半格.因此,关于C-rpp半群和Clifford半群的相应结构定理得到了推广.接着,本文还把格林L^(**)-关系和格林L^o-关系同时推广到了格林L^(oo)-关系,定义了C o-wrpp半群,并给出了这类半群的一个结构定理,从而推广了关于C-wrpp半群相应的结构定理.In this paper, a class of semigroups called C o-rpp semigroups which properly conclude the one of C-rpp semigroups are introduced first. It is shown that a semigroup S is a C o-rpp semigroup in which L° （S） is a right congruence if and only if it is a strong semilattice of left o-monoids. Consequently, the corresponding structure theorems of C-rpp semigroups and Clifford semigroups are extended and generalized. And then, Green＇s L^＊＊-relation and Green＇s L°-relation are generalized to Green＇s L°°-relation. Another class of semigroups called C o-wrpp semigroups are presented, and a structure theorem which generalizes the corresponding one of C-wrpp semigroups is also given.

关 键 词：C o-rpp半群 C o-wrpp半群 强半格 左o-幺半群 

分 类 号：O152.7[理学—数学]