On strongly pi-regular rings of stable range one
1995 ◽
Vol 51
(3)
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pp. 433-437
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An associative ring R is said to have stable range one if for any a, b ∈ R satisfying aR + bR = R, there exists y ∈ R such that a + by is right (equivalently, left) invertible. Call a ring R strongly π-regular if for every element a ∈ R there exist a number n (depending on a) and an element x ∈ R such that an = an+1x. It is an open question whether all strongly π-regular rings have stable range one. The purpose of this note is to prove the following Theorem: If R is a strongly π-regular ring with the property that all powers of every nilpotent von Neumann regular element are von Neumann regular in R, then R has stable range one.
2013 ◽
Vol 13
(01)
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pp. 1350072
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1974 ◽
Vol 19
(1)
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pp. 89-91
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1974 ◽
Vol 17
(2)
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pp. 283-284
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2006 ◽
Vol 2006
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pp. 1-6
Keyword(s):
1971 ◽
Vol 4
(1)
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pp. 57-62
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Keyword(s):
1969 ◽
Vol 12
(4)
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pp. 417-426
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Keyword(s):
Keyword(s):