On the number of generators of modules over polynomial rings
Author:
Hongnian Li
Journal:
Proc. Amer. Math. Soc. 121 (1994), 347351
MSC:
Primary 13E15; Secondary 13F20
MathSciNet review:
1213864
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Abstract: In this paper we prove the following Theorem. Let , where A is a universally catenary equidimensional ring. Let M be a finitely generated Bmodule of rank r. Denote by d the Krull dimension of A, by the minimal number of generators of M, and by the (radical) ideal which defines the set of primes of B at which M is not locally free. Assume that where is a positive integer. Then . This improves a result of R. G. López, On the number of generators of modules over polynomial affine rings, Math. Z. 208 (1991), 1121.
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Ricardo
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 s. M. Bhatwadekar and A. Roy, Some theorems about projective modules over polynomial rings, J. Algebra 86 (1986), 150158. MR 727374 (86m:13016)
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 R. G. López, On the number of generators of modules over polynomial affine rings, Math. Z. 208 (1991), 1121. MR 1125729 (93b:13033)
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 H. Matsumura, Commutative ring theory, Cambridge Stud. Adv. Math., vol. 8, Cambridge Univ. Press, Cambridge and New York, 1986. MR 879273 (88h:13001)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199412138646
PII:
S 00029939(1994)12138646
Keywords:
Number of generators,
modules,
polynomial rings,
universal catenary rings
Article copyright:
© Copyright 1994
American Mathematical Society
