Journal ArticleDOI
On injective and surjective endomorphisms of finitely generated modules
TLDR
In this paper, the authors studied injective and surjective endomorphisms of finitely generated modules and showed that they can be expressed as a set of endomorphism.Abstract:
(1978). On injective and surjective endomorphisms of finitely generated modules. Communications in Algebra: Vol. 6, No. 7, pp. 659-672.read more
Citations
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Strongly clean rings and fitting's lemma
TL;DR: In this paper, a natural generalization of strongly π-regular rings, called strongly clean regular rings, is presented. But their relationship to Fitting's lemma is not discussed.
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On semilocal rings
Rosa Camps,Warren Dicks +1 more
TL;DR: In this paper, the authors give several characterizations of semilocal rings and deduce that rationally closed subrings of semisimple artinian rings are semilecable.
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Stable range one for rings with many units
Ken R. Goodearl,Pere Menal +1 more
TL;DR: The main purpose of as mentioned in this paper is to prove the stable range 1 condition for a number of classes of rings and algebras, which is a modification of a computation of D.V. Tyukavkin.
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Strongly -regular rings have stable range one
TL;DR: In this article, it was shown that every strongly π-regular ring has stable range one, provided that, for any a, b ∈ R with aR + bR = R, there exists y ∈ r such that a+by is invertible in R.
Journal ArticleDOI
A crash course on stable range, cancellation, substitution and exchange
TL;DR: In this article, the authors provide a quick and relatively self-contained introduction to the voluminous work in this area, using the notion of the stable range of rings as a unifying tool.
References
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Journal ArticleDOI
On finitely generated flat modules
TL;DR: In this paper, the authors study conditions which reflect the projectivity of a given finitely generated flat module over a commutative ring and show that the invariant factors of a flat module are very peculiar (locally they are either (1) or (0)), the presence of almost any other condition on the module precipitates their finite generation.
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On the von Neumann regularity of rings with regular prime factor rings
Joe W. Fisher,Robert L. Snider +1 more
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