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Bounding the number of generators for a class of ideals in local rings

1995
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Communications in Algebra
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A well-known property of local (Noetherian) rings of dimension one is that there is, for each such ring, a number which uniformly bounds the number of generators of any ideal in the ring. A proof may be found in [7] (Theorem 1.2 of Chapter 3). In this paper we use the notation µ(I) for the minimal number of elements needed to generate an ideal I in a local ring R. Thus µ(I) = (I/mI), where m is the maximal ideal in R. In [2] we proved that, when R is one-dimensional, we actually have µ(I) ≤

doi:10.1080/00927879508825289
fatcat:rokq7zukyrflrhoezfkxy37wwe