A bracket power characterization of analytic spread one ideals
Authors:
L. J. Ratliff Jr. and D. E. Rush Jr.
Journal:
Trans. Amer. Math. Soc. 352 (2000), 16471674
MSC (1991):
Primary 13A15, 13B20, 13C10; Secondary 13H99
Published electronically:
July 26, 1999
MathSciNet review:
1641107
Fulltext PDF Free Access
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Abstract: The main theorem characterizes, in terms of bracket powers, analytic spread one ideals in local rings. Specifically, let be regular nonunits in a local (Noetherian) ring and assume that , the integral closure of , where . Then the main result shows that for all but finitely many units in that are noncongruent modulo and for all large integers and it holds that for and not divisible by , where is the th bracket power of . And, conversely, if there exist positive integers , , and such that has a basis such that , then has analytic spread one.
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Additional Information
L. J. Ratliff Jr.
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521
Email:
ratliff@math.ucr.edu
D. E. Rush Jr.
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521
Email:
rush@math.ucr.edu
DOI:
http://dx.doi.org/10.1090/S0002994799024344
PII:
S 00029947(99)024344
Keywords:
Analytic spread,
asymptotic prime divisor,
binomial coefficient,
bracket power of an ideal,
essential prime divisor,
integral closure of an ideal,
local ring,
Noetherian ring,
persistent prime divisor,
prenormal ideal,
projectively equivalent ideals,
RatliffRush closure of an ideal,
reduction of an ideal,
superficial element
Received by editor(s):
December 20, 1997
Published electronically:
July 26, 1999
Article copyright:
© Copyright 2000
American Mathematical Society
