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CS-modules and annihilator conditions

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  • Mahmoud A. Kamal
  • Amany M. Menshawy

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.

Suggested Citation

  • Mahmoud A. Kamal & Amany M. Menshawy, 2003. "CS-modules and annihilator conditions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:721079
    DOI: 10.1155/S0161171203206219
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