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.
出处
《数学进展》
CSCD
北大核心
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
