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Bull. Korean Math. Soc. 2009; 46(5): 873-884

Printed September 1, 2009

https://doi.org/10.4134/BKMS.2009.46.5.873

Copyright © The Korean Mathematical Society.

On $QB$-ideals of exchange rings

Huanyin Chen

Hangzhou Normal University

Abstract

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We characterize $QB$-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every $2\times 2$ matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange $QB$-rings are studied as well.

Keywords: $QB$-ideal, exchange ring, annihilator, diagonal reduction

MSC numbers: 16E50, 19B10

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