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Projective modules over group rings

✍ Scribed by Pramod K Sharma


Publisher
Elsevier Science
Year
1971
Tongue
English
Weight
547 KB
Volume
19
Category
Article
ISSN
0021-8693

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For several classes of commutative rings R it is known that every finitely generated projective R-modules is isomorphic to a direct sum of a free w x R-module and an invertible ideal of R. For instance, Steinitz 27 essenw x tially proved this for Dedekind domains. Serre 25 proved the same result for

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## Abstract We give a constructive proof of the fact that finitely generated projective modules over a polynomial ring with coefficients in a PrΓΌfer domain **R** with Krull dimension ≀ 1 are extended from **R**. In particular, we obtain constructively that finitely generated projective **R**[__X__~