EXCHANGE RINGS SATISFYING STABLE RANGE CONDITIONS

Title & Authors
EXCHANGE RINGS SATISFYING STABLE RANGE CONDITIONS
Chen, Huanyin; Chen, Miaosen;

Abstract
In this paper, we establish necessary and sufficient conditions for an exchange ring R to satisfy the n-stable range condition. It is shown that an exchange ring R satisfies the n-stable range condition if and only if for any regular a $\small{\in}$ R$\small{^n}$, there exists a unimodular u $\small{\in}$$\small{^n}$ R such that au $\small{\in}$ R is a group member, and if and only if whenever a$\small{\simeq}$$\small{_n}$b with a $\small{\in}$ R, b $\small{\in}$ M$\small{_n}$(R), there exist u $\small{\in}$ R$\small{^n}$, v $\small{\in}$$\small{^n}$ R such that a
Keywords
exchange ring;stable range condition;n-pseudo similarity;
Language
English
Cited by
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2.
A general vectorial Ekeland’s variational principle with a P-distance, Acta Mathematica Sinica, English Series, 2013, 29, 9, 1655
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