On N0-quasi-continuous exchange rings
作者:
Hua-Ping Yu,
期刊:
Communications in Algebra
(Taylor Available online 1995)
卷期:
Volume 23,
issue 6
页码: 2187-2197
ISSN:0092-7872
年代: 1995
DOI:10.1080/00927879508825340
出版商: Marcel Dekker, Inc.
关键词: Continuous Ring;Exchange Ring;Stable range one;Primary 16D70;16P70
数据来源: Taylor
摘要:
An associative ring R with identity is said to have stable range one if for any a,b∈ R with aR + bR = R, there exists y ∈ R such that a + by is left (equivalently, right) invertible. The main results of this note are Theorem 2: A left or right continuous ring R has stable range one if and only if R is directly finite (i.e xy = 1 implies yx = 1 for all x,y ∈ R), Theorem 6: A left or rightN0o-quasi-continuous exchange ring has stable range one if and only if it is directly finite, and Theorem 12: left or rightN0-quasi-continuous strongly π-regular rings have stable range one. Theorem 6 generalizes a well-known result of Goodearl [10], which says that a directly finite, rightNo-continuous von Neumann regular ring is unit-regular
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