CS-modules and annihilator conditions

Mahmoud A. Kamal and Amany M. Menshawy

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-8

Abstract:

We study S − R -bimodules S M R with the annihilator condition S = l S ( A ) + l S ( B ) for any closed submodule A , and a complement B of A , in M R . Such annihilator condition has a direct connection with the CS-condition for M R . We make use of this to give a new characterization of CS-modules. Bimodules S M R for which r M l S ( A ) = A (for every closed submodule A of M R ) 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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:721079

DOI: 10.1155/S0161171203206219

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