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完全■-单半群
引用本文:马思遥,任学明,袁莹.完全■-单半群[J].数学学报,2011(4):643-650.
作者姓名:马思遥  任学明  袁莹
作者单位:西安建筑科技大学数学系;
基金项目:国家自然科学基金资助项目(10971160)
摘    要:完全■-单半群是完全单半群和完全■~*-单半群在U-半富足半群类中的一个自然推广.本文证明了半群S是完全■-单半群,当且仅当S同构于幺半群T上的正规Rees矩阵半群■(T;I,A;P).这一结果不仅推广了完全单半群的著名Rees定理,而且推广了任学明和岑嘉评在2004年建立的完全■~*-单半群的一个结构定理.

关 键 词:U-超富足半群  完全■-单半群  正规Rees矩阵半群

On Completely ■-Simple Semigroups
Si Yao MA Xue Ming REN Ying YUAN.On Completely ■-Simple Semigroups[J].Acta Mathematica Sinica,2011(4):643-650.
Authors:Si Yao MA Xue Ming REN Ying YUAN
Institution:Si Yao MA Xue Ming REN Ying YUAN Department of Mathematics,Xi'an University of Architecture and Technology,Xi'an 710055,P.R.China
Abstract:Completely■-simple semigroups are natural generalizations of completely simple semigroups and completely■*-simple semigroups.In this paper,it is proved that a semigroup S is completely■-simple if and only if S is isomorphic to a normal Rees matrix semigroup M(T;I,■;P) over a monoid T.This result not only generalizes the well-known Rees theorem of completely simple semigroups,but also extends the structure theorem given by Ren and Shum in 2004 of completely■~*-simple semigroups.
Keywords:U-superabundant semigroups  completely ■-simple semigroups  normal Rees matrix
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