环的QG-根

QG-Radicals of Rings

本文定义环R的QG—根为R的所有Small理想之和,它适应于非结合环。定理2和5给出了QG(R)和QG—半单环的刻划,定理3和4给出了QG(R)和Jacobson与Brown—McCoy根及的一般根论的联系,定理1和8给出了一个环分解成单环直和的苦干充要条件,最后,定义投射环和拟半完备环的概念,从而给出一个关于QG(R)是R的Small理想的充分条件。

In this paper we have defined the QG-radical QG (R) of a ring R is the sum of all Small ideals of R. It applies to non-associative rings. The structures of QG ( R ) and QG-semisimple rings were given in the theorems 2 and5. We have given the relations between the QG-radical and Jacobson and Brown-McCoy radicals in the theorems 3 and 4. Finally, we have defined the protective ring and the Quasi-semiperfect ring, and have given a sufficient condition that the QG(R)will be a small ideal of R.