一些内-∑环的结构

Structure of Some Inner-∑xings

本文中约定不含真子环的环不是内-∑环. 定义1 设∑是某个代数性质,如果环R的任一页子环都具有性质∑,但R不具有性质∑,则R叫做一个内-∑环. 引理1 内除环是半单环. 引理2 内除环恰为两个单纯理想的直和. 推论内域环是半单环,内域环恰为两个单纯理想的直和. 引理3 非零环R不含真子环的充要条件是R为p元域或p元零乘环,这里p为素数.

In this paper the structure of four kinds of inner-∑ rings is discussed, The following main results are obtained: A ring R is inner-having no zero divisor-ring iff R=S_1S_2, where S_i is fields of prime order, and R is inner-finite-ring, then R is an indecomposable ring the quotient ring of which is an inner-finife-ring.