International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 469725, 7 pages
doi:10.1155/2008/469725
Research Article

AGQP-Injective Modules

Zhanmin Zhu1 and Xiaoxiang Zhang2

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.

Abstract

Let R be a ring and let M be a right R-module with S = End(MR). 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 Xsn of S such that sn≠0 and lS(Ker(sn))=Ssn⊕Xsn. Some characterizations and properties of AGQP-injective modules are given, and some properties of AGQP-injective modules with additional conditions are studied.