Ideals contracted from 1-dimensional overrings with an application to the primary decomposition of ideals, preprint [3 citations — 3 self]
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Abstract:
Abstract. We prove that each ideal of a locally formally equidimensional analytically unramified Noetherian integral domain is the contraction of an ideal of a one-dimensional semilocal birational extension domain. We give an application to a problem concerning the primary decomposition of powers of ideals in Noetherian rings. It is shown in [S2] that for each ideal I in a Noetherian commutative ring R there exists a positive integer k such that, for all n 1, there exists a primary decomposition I n = Q1 " \Delta \Delta \Delta " Qs where each Q i contains the nk-th power of its radical. We give an alternate proof of this result in the special case where R is locally at each prime ideal formally equidimensional and analytically unramified. In this paper we prove that every ideal in a locally formally equidimensional analytically unramified Noetherian ring R is the contraction of an ideal of a one-dimensional semilocal extension which is essentially of finite type over R. If R is a domain, the extension may be taken to be birational, i.e., with the same field of fractions as R. By passing to the extended Rees ring R[It; t
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