ON INJECTIVITY AND P-INJECTIVITY

Title & Authors
ON INJECTIVITY AND P-INJECTIVITY
Xiao Guangshi; Tong Wenting;

Abstract
The following results ale 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, $\small{_R(M/Z(M))}$ is projective, where Z(M) is the left singular submodule of $\small{_{R}M}$; (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 Y J-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;
Language
English
Cited by
1.
ON INJECTIVITY AND P-INJECTIVITY, IV,;

대한수학회보, 2003. vol.40. 2, pp.223-234
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