On injectivity and $P$-injectivity
Bull. Korean Math. Soc. 2006 Vol. 43, No. 2, 299-307
Published online June 1, 2006
Guangshi Xiao and Wenting Tong
Nanjing University of Aeronautics and Astronautics, Nanjing University
Abstract : The following results are extended from $P$-injective rings to $AP$-injective rings: (1) $R$ is left self-injective regular if and only if $R$ is a right (resp. left) $AP$-injective ring such that for every finitely generated left $R$-module $M$, $_{R}(M/Z(M))$ is projective, where $Z(M)$ is the left singular submodule of $_{R}M$; (2) if $R$ is a left nonsingular left $AP$-injective ring such that every maximal left ideal of $R$ is either injective or a two-sided ideal of $R$, then $R$ is either left self-injective regular or strongly regular. In addition, we answer a question of Roger Yue Chi Ming [13] in the positive. Let $R$ be a ring whose every simple singular left $R$-module is $YJ$-injective. If $R$ is a right $MI$-ring whose every essential right ideal is an essential left ideal, then $R$ is a left and right self-injective regular, left and right $V$-ring of bounded index.
Keywords : von Neumann regular rings, $P$-injective rings, $YJ$-injective rings, $AP$-injective rings
MSC numbers : 16D40, 16D50, 16E50
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd