On Rings with the Goodearl-Menal Condition

摘要

A ring R is said to satisfy the Goodearl-Menal condition if for any x, y  R, there exists a unit u of R such that both x − u and y − u −1 are units of R. It is proved that if R is a semilocal ring or an exchange ring with primitive factors Artinian, then R satisfies the Goodearl-Menal condition if and only if no homomorphic image of R is isomorphic to either ₂ or ₃ or ₂(₂). These results correct two existing results. Some consequences are discussed.View full textDownload full textKey WordsGoodearl-Menal condition, Matrix ring, Semilocal ring, Unit, Unit 1-stable range2010 Mathematics Subject ClassificationPrimary 16S50, 16U99Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927872.2011.618856