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 transver...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.展开更多
A right adequate semigroup of type F is defined as a right adequate semigroup which is an F-rpp semigroup. A right adequate semigroup T of type F is called an F-cover for a right type-A semigroup S if S is the image o...A right adequate semigroup of type F is defined as a right adequate semigroup which is an F-rpp semigroup. A right adequate semigroup T of type F is called an F-cover for a right type-A semigroup S if S is the image of T under an L＊-homomorphism. In this paper, we will prove that any right type-A monoid has F-covers and then establish the structure of F-covers for a given right type-A monoid. Our results extend and enrich the related results for inverse semigroups.展开更多
In this paper, we study ＊-simple type A ω2 -semigroups in which D＊= D and D＊｜ES = Md by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two ...In this paper, we study ＊-simple type A ω2 -semigroups in which D＊= D and D＊｜ES = Md by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two such semigroups.展开更多
基金Supported by National Natural Science Foundation of China of China(Grant No.10961014)Natural Science Foundation of Jiangxi Provincethe SF of Education Department of Jiangxi Province,China(Grant No.GJJ11388)
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant No.10961014)the Natural Science Foundation of Jiangxi Province (Grant No.2008GZ048)+1 种基金the Science Foundation of the Education Department of Jiangxi Province and the Foundation of Jiangxi Normal University (Grant No.[2007]134)the Graduate Innovation Special Foundation of the Education Department of Jiangxi Province (Grant No.YC08A044)
文摘A right adequate semigroup of type F is defined as a right adequate semigroup which is an F-rpp semigroup. A right adequate semigroup T of type F is called an F-cover for a right type-A semigroup S if S is the image of T under an L＊-homomorphism. In this paper, we will prove that any right type-A monoid has F-covers and then establish the structure of F-covers for a given right type-A monoid. Our results extend and enrich the related results for inverse semigroups.
基金The NSF (10901134) of Chinathe Science Foundation (2011Y478) of the Department of Education of Yunnan Province
文摘In this paper, we study ＊-simple type A ω2 -semigroups in which D＊= D and D＊｜ES = Md by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two such semigroups.
基金Supported by the National Natural Science Foundation of China(10901134)the Science Foundation of the Department of Education of Yunnan Province(2011Y478)
