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Original Articles

Separativity of Regular Rings in Which 2 Is Invertible

Pages 1661-1673 | Received 31 Jan 2006, Published online: 07 May 2007
 

Abstract

A regular ring R is separative provided that for all finitely generated projective right R-modules A and B, AAABAB implies that AB. We prove, in this article, that a regular ring R in which 2 is invertible is separative if and only if each a ∈ R satisfying R(1 − a 2)R = Rr(a) = ℓ(a)R and i(End R (aR)) = ∞ is unit-regular if and only if each a ∈ R satisfying R(1 − a 2)R ∩ RaR = Rr(a) ∩ ℓ(a)R ∩ RaR and i(End R (aR)) = ∞ is unit-regular. Further equivalent characterizations of such regular rings are also obtained.

2000 Mathematics Subject Classification:

Notes

Communicated by V. A. Artamonov.

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