Reductions of ideals in local rings with finite residue fields
Authors:
William J. Heinzer, Louis J. Ratliff Jr. and David E. Rush
Journal:
Proc. Amer. Math. Soc. 138 (2010), 15691574
MSC (2000):
Primary 13A15, 13E05, 13H10
Published electronically:
January 8, 2010
MathSciNet review:
2587440
Fulltext PDF
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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 .
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Additional Information
William J. Heinzer
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 479071395
Email:
heinzer@math.purdue.edu
Louis J. Ratliff Jr.
Affiliation:
Department of Mathematics, University of California, Riverside, California 925210135
Email:
ratliff@math.ucr.edu
David E. Rush
Affiliation:
Department of Mathematics, University of California, Riverside, California 925210135
Email:
rush@math.ucr.edu
DOI:
http://dx.doi.org/10.1090/S0002993910100501
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
Published electronically:
January 8, 2010
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2010
American Mathematical Society
