Ideals contracted from 1-dimensional

overrings with an application

to the primary decomposition of ideals

Authors:
William Heinzer and Irena Swanson

Journal:
Proc. Amer. Math. Soc. **125** (1997), 387-392

MSC (1991):
Primary 13C05, 13E05, 13H99

DOI:
https://doi.org/10.1090/S0002-9939-97-03703-9

MathSciNet review:
1363423

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Abstract | References | Similar Articles | Additional Information

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 an earlier paper by the second author that for each ideal in a Noetherian commutative ring there exists a positive integer such that, for all , there exists a primary decomposition where each contains the -th power of its radical. We give an alternate proof of this result in the special case where is locally at each prime ideal formally equidimensional and analytically unramified.

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Additional Information

**William Heinzer**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

Email:
heinzer@math.purdue.edu

**Irena Swanson**

Affiliation:
Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003-8001

Email:
iswanson@nmsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03703-9

Received by editor(s):
September 6, 1995

Additional Notes:
The authors thank Craig Huneke for helpful suggestions concerning this paper.

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1997
American Mathematical Society