International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 50, Pages 3195-3202
CS-modules and annihilator conditions
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Received 4 June 2002
Copyright © 2003 Mahmoud A. Kamal and Amany M. Menshawy. 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.
We study -bimodules with the
annihilator condition for any closed submodule
, and a complement of , in . Such annihilator
condition has a direct connection with the CS-condition for
. We make use of this to give a new characterization of
CS-modules. Bimodules for which (for
every closed submodule of ) are also dealt with. Such
modules are called -modules. We give the extra added
annihilator conditions to -modules to be equivalent to the
continuous (quasicontinuous) modules.