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Gorenstein rings and irreducible parameter ideals
Author(s):
Thomas
Marley;
Mark
W.
Rogers;
Hideto
Sakurai
Journal:
Proc. Amer. Math. Soc.
136
(2008),
49-53.
MSC (2000):
Primary 13D45;
Secondary 13H10
Posted:
September 27, 2007
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Abstract:
Given a Noetherian local ring  it is shown that there exists an integer  such that  is Gorenstein if and only if some system of parameters contained in  generates an irreducible ideal. We obtain as a corollary that  is Gorenstein if and only if every power of the maximal ideal contains an irreducible parameter ideal.
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Additional Information:
Thomas
Marley
Affiliation:
Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588-0130
Email:
tmarley@math.unl.edu
Mark
W.
Rogers
Affiliation:
Department of Mathematics, Missouri State University, Springfield, Missouri 65897
Email:
markrogers@missouristate.edu
Hideto
Sakurai
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, 214-8571, Japan
Email:
hsakurai@math.meiji.ac.jp
DOI:
10.1090/S0002-9939-07-08958-7
PII:
S 0002-9939(07)08958-7
Keywords:
Gorenstein,
system of parameters,
irreducible ideal
Received by editor(s):
August 25, 2006
Received by editor(s) in revised form:
September 21, 2006
Posted:
September 27, 2007
Additional Notes:
The second author was supported for eight weeks during the summer of 2006 through the University of Nebraska-Lincoln's \it Mentoring through Critical Transition Points \rm grant (DMS-0354281) from the National Science Foundation.
Dedicated:
Dedicated to Professor Shiro Goto on the occasion of his sixtieth birthday
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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