Exchange rings having stable range one.
Chen, Huanyin (2001)
International Journal of Mathematics and Mathematical Sciences
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Chen, Huanyin (2001)
International Journal of Mathematics and Mathematical Sciences
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Huanyin Chen, Fu-An Li (2002)
Collectanea Mathematica
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In this paper we investigate the related comparability over exchange rings. It is shown that an exchange ring R satisfies the related comparability if and only if for any regular x C R, there exists a related unit w C R and a group G in R such that wx C G.
Chen, Huanyin, Li, Fu-an (2001)
International Journal of Mathematics and Mathematical Sciences
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Heatherly, H.E., Courville, J.R. (1999)
Mathematica Pannonica
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Huanyin Chen (2007)
Czechoslovak Mathematical Journal
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We characterize exchange rings having stable range one. An exchange ring has stable range one if and only if for any regular , there exist an and a such that and if and only if for any regular , there exist and such that if and only if for any , .
Huanyin Chen (2008)
Czechoslovak Mathematical Journal
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Let be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.