International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 50, Pages 3195-3202
doi:10.1155/S0161171203206219
CS-modules and annihilator conditions.
Mahmoud A. Kamal
and Amany M. Menshawy
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Abstract
We study S−R-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.