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
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.
