Elements in exchange rings with related comparability

Huanyin Chen

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-6

Abstract:

We show that if R is an exchange ring, then the following are equivalent: (1) R satisfies related comparability. (2) Given a , b , d ∈ R with a R + b R = d R , there exists a related unit w ∈ R such that a + b t = d w . (3) Given a , b ∈ R with a R = b R , there exists a related unit w ∈ R such that a = b w . Moreover, we investigate the dual problems for rings which are quasi-injective as right modules.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:413021

DOI: 10.1155/S0161171200002234

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