Local comparability of exchange ideals

Date
2019
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Source Title
International Electronic Journal of Algebra
Print ISSN
1306-6048
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Publisher
Hacettepe University
Volume
25
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Pages
1 - 11
Language
English
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Abstract

An exchange ideal I of a ring R is locally comparable if for every regular x ∈ I there exists a right or left invertible u ∈ 1+I such that x = xux. We prove that every matrix extension of an exchange locally comparable ideal is locally comparable. We thereby prove that every square regular matrix over such ideal admits a diagonal reduction.

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