The number of generators of modules over polynomial rings

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)1037-1040
Number of pages4
JournalProceedings of the American Mathematical Society
Volume103
Issue number4
DOIs
StatePublished - Aug 1988

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