Rings for Which Certain Elements Have the Principal Extension Property

• 来源期刊: 代数集刊（英文版）
• 关键词: JP-injective rings GC2-condition chain conditions on annihilators
• 年，卷（期）: 2003,（4）
• 页码范围: 501-512
• 页数: 12页
• 语种: 英文

摘要

For a ring R, let p(RR) = {a ∈ R: lr(a) = Ra}. It is known that R is right P-injective if and only if p(RR) = R, and R is right mininjective if and only if {a ∈ R: aR is simple} p(RR). In this paper, we investigate the ring R for which J(R) p(RR) or {a ∈ R: r(a) = 0} p(RR). Various properties of the two ring concepts are obtained and several known results of right P-injective and right continuous rings are extended.2000 Mathematics Subject Classification: 16D50, 16P60