CLOSED SUBMODULES OF NORMALIZING BIMODULES OVER SEMIPRIME RINGS

Abstract

In this paper we study closed sub-bimodules of normalizing bimodules over semiprime rings. We extend the main results which are known for centred bimodules and several other results which are new even for centred bimodules are also obtained. In particular, we prove that the theorem on one-to-one correspondence between closed submodules obtained in former papers for centred bimodules is also true for normalizing bimodules. Finally, we give some applications of the main results.

^*Partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil).

Keywords:

• 1991 Mathematics Subject Classification: 16D20, 16S90

ACKNOWLEDGMENT

The author is grateful to the referee for several suggestions that helped to improve the final version of this paper.

Notes

^*Partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil).