【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) y更多还原

【Abstract】 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.更多还原