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International Journal of Mathematics and Mathematical Sciences
Volume 2008, Article ID 469725, 7 pages
Research Article

AGQP-Injective Modules

1Department of Mathematics, Jiaxing University, Jiaxing, Zhejiang 314001, China
2Department of Mathematics, Southeast University, Nanjing 210096, China

Received 23 December 2007; Revised 20 April 2008; Accepted 20 June 2008

Academic Editor: Robert Lowen

Copyright © 2008 Zhanmin Zhu and Xiaoxiang Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let 𝑅 be a ring and let 𝑀 be a right 𝑅 -module with 𝑆 = End( 𝑀 𝑅 ). 𝑀 is called almost general quasi-principally injective (or AGQP-injective for short) if, for any 0 𝑠 𝑆 , there exist a positive integer 𝑛 and a left ideal 𝑋 𝑠 𝑛 of 𝑆 such that 𝑠 𝑛 0 and 𝐥 𝑆 ( K e r ( 𝑠 𝑛 ) ) = 𝑆 𝑠 𝑛 𝑋 𝑠 𝑛 . Some characterizations and properties of AGQP-injective modules are given, and some properties of AGQP-injective modules with additional conditions are studied.