Gorenstein rings and irreducible parameter ideals
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- by Thomas Marley, Mark W. Rogers and Hideto Sakurai PDF
- Proc. Amer. Math. Soc. 136 (2008), 49-53 Request permission
Abstract:
Given a Noetherian local ring $(R,m)$ it is shown that there exists an integer $\ell$ such that $R$ is Gorenstein if and only if some system of parameters contained in $m^{\ell }$ generates an irreducible ideal. We obtain as a corollary that $R$ is Gorenstein if and only if every power of the maximal ideal contains an irreducible parameter ideal.References
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Additional Information
- Thomas Marley
- Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588-0130
- MR Author ID: 263869
- 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
- Received by editor(s): August 25, 2006
- Received by editor(s) in revised form: September 21, 2006
- Published electronically: 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 Mentoring through Critical Transition Points grant (DMS-0354281) from the National Science Foundation.
- Communicated by: Bernd Ulrich
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 49-53
- MSC (2000): Primary 13D45; Secondary 13H10
- DOI: https://doi.org/10.1090/S0002-9939-07-08958-7
- MathSciNet review: 2350387
Dedicated: Dedicated to Professor Shiro Goto on the occasion of his sixtieth birthday