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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 50, Pages 3195-3202
http://dx.doi.org/10.1155/S0161171203206219

CS-modules and annihilator conditions

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Received 4 June 2002

Copyright © 2003 Hindawi Publishing Corporation. 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

We study SR-bimodules SMR with the annihilator condition S=lS(A)+lS(B) for any closed submodule A, and a complement B of A, in MR. Such annihilator condition has a direct connection with the CS-condition for MR. We make use of this to give a new characterization of CS-modules. Bimodules SMR for which rMlS(A)=A (for every closed submodule A of MR) are also dealt with. Such modules are called W-modules. We give the extra added annihilator conditions to W-modules to be equivalent to the continuous (quasicontinuous) modules.