P_2-环A的所有子环还是P_2-环的条件

THE CONDITATION THAT ALL SUBRINGS OF P_2-RING ARE AGAIN P_2-RING

本文讨论了Ferenc·Szasz提出的问题(3)何种P_2-环的所有子环还是P_2-环.证明了如下结论:强正则环,P_1-环和具有唯一自反逆的正则环是P_2-环.而且若它们满足条件:1.P_2-环A的子环均是A的理想.或2.P_2-环A的子环N的理想均是A的理想.那么它们的所有子环还是P_2-环.

In this paper, we discuss the problem (3) that was asked by Ferenc Szasz at Math Japoinace in 1972, we obtain the following results. When A is P1-ring (strongly regular ring, regular ring that has unique reflesive inverse) all subrings of A-ring are again P2-ring it A-ring possess following conditations. 1. subrings of A-ring are ideas of A-ring, or 2. ideas of subrings of A-ring are ideas of A-ring.