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Reductions of ideals in local rings with finite residue fields
Author(s):
William
J.
Heinzer;
Louis
J.
Ratliff Jr.;
David
E.
Rush
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1569-1574.
MSC (2000):
Primary 13A15, 13E05, 13H10
Posted:
January 8, 2010
MathSciNet review:
2587440
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Abstract:
Let  be a proper nonnilpotent ideal in a local (Noetherian) ring  and let  be a reduction of  ; that is,    and    for some nonnegative integer  . We prove that there exists a finite free local unramified extension ring  of  such that the ideal  has a minimal reduction    with the property that the number of elements in a minimal generating set of  is equal to the analytic spread of  and thus also equal to the analytic spread of  .
References:
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- W. Bruns and J. Herzog, Cohen-Macaulay Rings, revised edition, Cambridge Univ. Press, Cambridge 1998. MR 1251956 (95h:13020)
- 2.
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Additional Information:
William
J.
Heinzer
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395
Email:
heinzer@math.purdue.edu
Louis
J.
Ratliff
Jr.
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521-0135
Email:
ratliff@math.ucr.edu
David
E.
Rush
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521-0135
Email:
rush@math.ucr.edu
DOI:
10.1090/S0002-9939-10-10050-1
PII:
S 0002-9939(10)10050-1
Keywords:
Minimal reduction,
analytic spread,
finite free local unramified extension,
Rees valuation rings,
projective equivalence of ideals
Received by editor(s):
February 13, 2009,
Received by editor(s) in revised form:
May 26, 2009
Posted:
January 8, 2010
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2010,
American Mathematical Society
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