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On the Smoothness of Generic Rings for Stably Free Modules

Published online by Cambridge University Press:  20 November 2018

Robert W. Swift
Robert W. Swift*
Affiliation:
Department of Mathematics University of Western Ontario, LondonOntario N6A 5B9
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Abstract

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We show certain generic rings for stably free modules are smooth. Using the theory of smooth algebras we deduce that these rings are regular when the base ring is regular. Also this enables us to calculate the dimensions of these rings. Gabel used these generic rings to determine the freeness of certain stably free modules. Our results allow a strengthening of his results when restrictions are placed on the type of stably free module—for example orthogonal stably free modules.

Keywords

13C10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 1 , 01 March 1982 , pp. 64 - 70
Copyright
Copyright © Canadian Mathematical Society 1982

References

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6. Swift, R., Smooth Algebras, M.Sc. Thesis?Queen's University, Kingston, 1978.Google Scholar