关于半群的广义Bruck-Reilly扩张  

On Generalized Bruck-Reilly Extension of Semigroup

作　　者：田振际[1] 黎锁平[1] 严克明[1] 

机构地区：[1]甘肃工业大学基础科学系,甘肃兰州730050

出　　处：《兰州大学学报（自然科学版）》2001年第5期10-14,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：甘肃工业大学博士基金

摘　　要：引进了半群的广义 Bruck- Reilly扩张的概念 ,研究了其简单性质 ;给出了半群的广义Bruck- Reilly扩张是π-逆半群的充要条件 ;刻画了一个半群 (逆半群 )Τ的广义 Bruck- Reilly扩张为单 (或半单 )半群时半群 (逆半群 ) T的性质 ,证明了由同态θ及幂等元 e0 所确定的半群 T的广义Bruck- Reilly扩张 BR(T,e0 ,θ)是单半群当且仅当对任意 a,b∈ T,存在 x ,y∈ T1以及 k∈ N使得a =x(bθk)The concept of generalized Bruck Reilly extension of semigroup is introduced. This paper deals with its simple character and shows that the generalized Bruck Reilly extension of semigroup is a sufficient condition for π inverse semigroup. It depicts the character of a semigroup(inverse semigroup) T when generalized Bruck Reilly extension of the semigroup (inverse semigroup) T is a simple (or semisimple)semigroup. It demonstrates that generalized Bruck Reilly extension BR(T,e 0,θ) of semigroup T determined by homomorphism θ and idempotent e 0 is a simple semigroup if and only if for every a,b∈T, there exist x,y∈T 1 and k∈N such that a=x(bθ k)y.

关 键 词：广义Bruck-Reilly扩张 Π-逆半群 单半群 半单半群 

分 类 号：O152.7[理学—数学]