TY - JOUR
T1 - The number of generators of modules over polynomial rings
AU - Lyubeznik, Gennady
PY - 1988/8
Y1 - 1988/8
N2 - Let k be an infinite field and B = k[X1,…, Xn] a polynomial ring over k. Let M be a finitely generated module over B. For every prime ideal P ⊂ B let μ(MP) be the minimum number of generators of Mp, i.e., μ(MP) = dimBP/PP(MP®BP (BP/PP)). Set η(M) = max(μ(MP) + dim(B/P)|P ∄ SpecB such that MP is not free). Then M can be generated by η(M) elements. This improves earlier results of A. Sathaye and N. Mohan Kumar on a conjecture of Eisenbud-Evans.
AB - Let k be an infinite field and B = k[X1,…, Xn] a polynomial ring over k. Let M be a finitely generated module over B. For every prime ideal P ⊂ B let μ(MP) be the minimum number of generators of Mp, i.e., μ(MP) = dimBP/PP(MP®BP (BP/PP)). Set η(M) = max(μ(MP) + dim(B/P)|P ∄ SpecB such that MP is not free). Then M can be generated by η(M) elements. This improves earlier results of A. Sathaye and N. Mohan Kumar on a conjecture of Eisenbud-Evans.
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U2 - 10.1090/S0002-9939-1988-0954979-4
DO - 10.1090/S0002-9939-1988-0954979-4
M3 - Article
AN - SCOPUS:84934258589
SN - 0002-9939
VL - 103
SP - 1037
EP - 1040
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 4
ER -