TY - JOUR

T1 - The number of generators of modules over polynomial rings

AU - Lyubeznik, Gennady

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

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

VL - 103

SP - 1037

EP - 1040

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -