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A note on right equivalence of module presentations

Published online by Cambridge University Press:  09 April 2009

M. J. Canfell
M. J. Canfell
Affiliation:
Department of Mathematics, Statistics and Computing ScienceUniversity of New EnglandArmidale, N.S.W. 2351, Australia
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Abstract

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If R has 1 in the stable range, then any two presentations f, g: p→ M of an R-module M by a finitely generated projective p are right equivalent, that is, f = gh for some automorphism h of P. The convers is also true.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 1 , February 1992 , pp. 141 - 142
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Vaserstein, L. N., ‘Bass's first stable range condition’, J. Pure Appl. Algebra 34 (1984), 319–330.CrossRefGoogle Scholar
[2]Warfield, R. B. Jr, ‘Stable equivalence of matrices and resolutions’, Comm. Algegbra 6 (1978), 1811–1828.CrossRefGoogle Scholar
[3]Warfield, R. B. Jr, ‘Stable generation of modules’, Lecture Notes in Mathematics 700, pp. 16–33 (Springer-Verlag, New York, 1979).Google Scholar