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A right continuous right weakly si-ring is semisimple

Published online by Cambridge University Press:  17 April 2009

Dinh Van Huynh  and
Nguyen Van Sanh
Dinh Van Huynh
Affiliation:
Institute of Mathematics, PO Box 631, Boho, Hanoi, Vietnam
Nguyen Van Sanh
Affiliation:
Department of Mathematics, Hue University of Pedagogy, 32 Le Loi St, Hue, Vietnam
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Abstract

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It is shown that a projective CS right module M over a ring R is a direct sum of uniform modules of composition lengths at most 2 if (i) every finitely generated direct summand of M is continuous and (ii) every non-zero M-singular right R-module contains a non-zero M-injective submodule. In particular, a right continuous ring R is semisimple if R is right weakly SI, that is, if every non-zero singular right R-module contains a non-zero injective submodule.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 3 , June 1995 , pp. 479 - 488
Copyright
Copyright © Australian Mathematical Society 1995

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