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3.—A Note on Projective Modules*

Published online by Cambridge University Press:  14 February 2012

P. F. Smith
Affiliation:
Department of Mathematics, University of Glasgow.

Synopsis

For various classes of right noetherian rings it is shown that projective right modules are either finitely generated or free.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

1Bass, H.. Big projective modules are free. Illinois J. Math. 7 (1963), 2431.CrossRefGoogle Scholar
2Bergman, G. M.. Infinite multiplication of ideals in ℵ-hereditary rings. J. Algebra 24 (1973), 5670.Google Scholar
3Goldie, A. W.. Semi-prime rings with maximum condition. Proc. London Math. Soc. 10 (1960), 201220.CrossRefGoogle Scholar
4Hinohara, Y.. Projective modules over semilocal rings. Tohoku Math. J. 14 (1962), 205211.CrossRefGoogle Scholar
5Jacobson, N.. The radical and semisimplicity for arbitrary rings. Amer. J. Math. 67 (1945), 300320.Google Scholar
6Jategaonkar, A. A counter-example in ring theory and homological algebra. J. Algebra 12 (1969), 418440.CrossRefGoogle Scholar
7Kaplansky, I.. Projective modules. Ann. of Math. 68 (1958), 372377.Google Scholar
8Roggenkamp, K. W.. Integral group rings of solvable finite groups have no idempotent ideals. Archiv Math. (Basel) 25 (1974), 125128.CrossRefGoogle Scholar
9Smith, P. F.. On the intersection theorem. Proc. London Math. Soc. 21 (1970), 385398.CrossRefGoogle Scholar
10Smith, P. F.. On the dimension of group rings. Proc. London Math. Soc. 25 (1972), 288302.CrossRefGoogle Scholar
11Swan, R. G.. The Grothendieck ring of a finite group. Topology 2 (1963), 85110.CrossRefGoogle Scholar
12Zariski, O. and Samuel, P.. Commutative algebra, I (Princeton: Van Nostrand, 1958).Google Scholar