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Stable Rings

Published online by Cambridge University Press:  20 November 2018

S. S. Page
S. S. Page*
Affiliation:
Department of Mathematics University of British Columbia, Vancouver B.C.V6T 1W5
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Let R be an associative ring with identity. If R is von- Neumann regular of a left v-ring, then for each left ideal, I, we have I2 = I. In this note we study rings such that for each left ideal L there exists an integer n = n(L)>0 such that Ln = Ln+1. We call such rings stable rings. We completely describe the stable commutative rings. These descriptions give rise to concepts related to, but more general than, finite Goldie dimension and T-nilpotence, and a notion of power pure.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 2 , 01 June 1980 , pp. 173 - 178
Copyright
Copyright © Canadian Mathematical Society 1980