A semigroup is called completely J（e）-simple if it is isomorphic to some Rees matrix semi- group over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellat...A semigroup is called completely J（e）-simple if it is isomorphic to some Rees matrix semi- group over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid. It is proved that completely J（e）-simple semigroups form a quasivarity. Moreover, the construction of free completely J（e）simple semigroups is given. It is found that a free completely J（e）-simple semigroup is just a free completely J＊-simple semigroup and also a full subsemigroup of some completely simple semigroups.展开更多
It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular...It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.展开更多
We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated...We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11361027)the Natural Science Foundation of Jiangxi Provincethe Science Foundation of the Education Department of Jiangxi Province,China
文摘A semigroup is called completely J（e）-simple if it is isomorphic to some Rees matrix semi- group over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid. It is proved that completely J（e）-simple semigroups form a quasivarity. Moreover, the construction of free completely J（e）simple semigroups is given. It is found that a free completely J（e）-simple semigroup is just a free completely J＊-simple semigroup and also a full subsemigroup of some completely simple semigroups.
基金supported by National Natural Science Foundation of China (Grant No.10571061)
文摘It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11371178） and the National Science Foundation of US （Grant No. DMS 1001855）.
文摘We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.
