Ideals contracted from 1dimensional overrings with an application to the primary decomposition of ideals
Authors:
William Heinzer and Irena Swanson
Journal:
Proc. Amer. Math. Soc. 125 (1997), 387392
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 onedimensional 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 479071395
Email:
heinzer@math.purdue.edu
Irena Swanson
Affiliation:
Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 880038001
Email:
iswanson@nmsu.edu
DOI:
http://dx.doi.org/10.1090/S0002993997037039
PII:
S 00029939(97)037039
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
