关于AP-内射环的一个注记(英文)

A Note on AP-Injective Rings

中文关键词:  AP-内射环  弱内射环  PP-环

英文关键词:AP-injective rings  weakly injective rings  PP-rings.

中文摘要:

      本文的主要目的是讨论AP-内射环中的两个问题:(1)环R是正则的当且仅当R是左AP-内射的左PP-环;(2)如果R是左AP-内射环,那么R是内射环当且仅当R是弱内射环.因此我们推广了内射环的一些结果,与此同时我们还取得了一些新的结果.

英文摘要:

      The purpose of this paper is to study the following two questions on AP-injective rings: (1) R is a regular ring if and only if R is a left PP-ring and R is left AP-injective; (2) Let R be a right .AP-injective ring. Then R is self-injective if and only if R is weakly injective. Hence we get some new results of P-injective rings.