α-GWS环

Study on α-GWS Rings

设α是环R的自同态,如果对任意的a,b,c∈R,若abc=0,有acα(b)∈N(R),则称R为α-GWS环.文中引入了α-GWS环的概念,并举例说明了α-GWS环是α-对称环的真推广,给出了α-GWS环的基本性质,得到了α-GWS环的一些刻画.

Let α be an endomorphism of the ring R, then R is called an α-GWS ring, if acoα（b） = 0, whenever abc = 0 for a, b, c ∈ R. In this study the notion of α-GWS rings was introduced. Some examples were given to explain that α-GWS rings are generalizations of α-symmetric rings. The basic properties of α-GWS rings were investigated, and some equivalent characterizations of α-GWS rings were obtained.