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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 1363423
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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 $I$ in a Noetherian commutative ring $R$ there exists a positive integer $k$ such that, for all $n \ge 1$, there exists a primary decomposition $I^{n} = Q_{1} \cap \dots \cap Q_{s}$ 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.

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Additional Information

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

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

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