Abelian Exchange Modules

Nielsen, Pace P.

doi:10.1081/agb-200053819

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Comments As Already Indicated the Exchange Property Was In1

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Cited by 10 publications

(2 citation statements)

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“…A positive answer was also recently given, in [27], for modules with abelian endomorphism rings. There seems to be an error in this paper, but the result has been reaffirmed by a different, and much shorter, proof by P. P. Nielsen [69].…”

Section: Epiloguesupporting

confidence: 55%

A Crash Course on Stable Range, Cancellation, Substitution and Exchange

Lam

2004

J. Algebra Appl.

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The themes of cancellation, internal cancellation, substitution and exchange have led to a lot of interesting research in the theory of modules over commutative and noncommutative rings. This article provides 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. With only a small number of exceptions, all theorems stated here are proved in full, modulo basic facts in the theory of modules and rings available in standard textbooks on ring theory.

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Section: Epiloguesupporting

confidence: 55%

A Crash Course on Stable Range, Cancellation, Substitution and Exchange

Lam

2004

J. Algebra Appl.

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“…An affirmative answer has also been provided for quasi-continuous modules by Oshiro and Rizvi [276] and then simplified by Mohamed and Müller [242] (although quasi-continuous modules need not enjoy the finite exchange property, as evidenced by the Z-module Z in Exercise (1) above). Yu [375] shows that if M has the finite exchange property and idempotents in End(M ) are all central (equivalently, all direct summands of M are fully invariant), then M has the ℵ0-exchange property and this has been recently extended to the full exchange property by Nielsen [263].…”

Section: Comments As Already Indicated the Exchange Property Was Inmentioning

confidence: 99%