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Rings with dual continuous right ideals

Published online by Cambridge University Press:  09 April 2009

Saad Mohamed
Saad Mohamed
Affiliation:
Department of Mathematics Kuwait UniversityKuwait
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Abstract

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In this paper the structure of rings with dual continuous right ideals is discussed. The main result is the following: If R is a ring with (Jacobson) radical nil, and all of its finitely generated right ideals are dual continuous, then where S is a finite direct sum of local rings each of which has its radical square zero, or is a right valuation ring, T is semiprimary right semihereditary ring, and M is an (S, T)-bimodule such that all of its finitely generated T-submodules are projective. A partial converse of this result is obtained: any matrix ring of the above type with M = 0 has all of its finitely generated right ideals dual continuous.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 3 , December 1982 , pp. 287 - 294
Copyright
Copyright © Australian Mathematical Society 1982

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