Abstract
For an ideal I in a noetherian ring R, let μ(I) be the minimal number of generators of I. It is well known that there is a sequence of inequalities μ(I/I) ≤ μ(I) ≤ μ(I/I) + 1 that are strict in general. However, Murthy conjectured in 1975 that μ(I/I) = μ(I) for ideals in polynomial rings whose height equals μ(I/I). The purpose of this article is to prove a stronger form of the conjecture in case the base field is infinite of characteristic different from 2: Namely, the equality μ(I/I) = μ(I) holds for any ideal I, irrespective of its height.
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