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
用V1,V2,V3和V4表示正规带的4个给定的拟簇.利用幂等元半环上的同余关系分别给出了.V1,.V2,.V3和.V4中成员的次直积分解和这些拟簇的M al'cev积分解,并借助Zhao X Z的"(2,2)型代数的坚固构架"理论揭示了.V1∩N.B,.V3∩中...用V1,V2,V3和V4表示正规带的4个给定的拟簇.利用幂等元半环上的同余关系分别给出了.V1,.V2,.V3和.V4中成员的次直积分解和这些拟簇的M al'cev积分解,并借助Zhao X Z的"(2,2)型代数的坚固构架"理论揭示了.V1∩N.B,.V3∩中.NB成员的次直积分解与坚固构架之间的密切联系。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 NSFC(No.11361027)the Natural Science Foundation of Jiangxi Province(No.2014BAB201009)+1 种基金the Science Foundation of the Education Department of Jiangxi Province(No.GJJ14251)the Graduate Innovation Foundation of Jiangxi Province(No,YC2014-S160)
文摘用V1,V2,V3和V4表示正规带的4个给定的拟簇.利用幂等元半环上的同余关系分别给出了.V1,.V2,.V3和.V4中成员的次直积分解和这些拟簇的M al'cev积分解,并借助Zhao X Z的"(2,2)型代数的坚固构架"理论揭示了.V1∩N.B,.V3∩中.NB成员的次直积分解与坚固构架之间的密切联系。
