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 On $QB$-ideals of exchange rings Bull. Korean Math. Soc. 2009 Vol. 46, No. 5, 873-884 https://doi.org/10.4134/BKMS.2009.46.5.873Printed September 1, 2009 Huanyin Chen Hangzhou Normal University Abstract : 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 Downloads: Full-text PDF