Detecting completeness from Ext-vanishing
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- by Anders J. Frankild and Sean Sather-Wagstaff
- Proc. Amer. Math. Soc. 136 (2008), 2303-2312
- DOI: https://doi.org/10.1090/S0002-9939-08-09199-5
- Published electronically: February 28, 2008
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Abstract:
Motivated by work of C. U. Jensen, R.-O. Buchweitz, and H. Flenner, we prove the following result. Let $R$ be a commutative noetherian ring and $\mathfrak {a}$ an ideal in the Jacobson radical of $R$. Let $\widehat {\mathfrak {Ra}}$ be the $\mathfrak {a}$-adic completion of $R$. If $M$ is a finitely generated $R$-module such that $\operatorname {Ext}^i_R( M)=0$ for all $i\neq 0$, then $M$ is $\mathfrak {a}$-adically complete.References
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Bibliographic Information
- Anders J. Frankild
- Affiliation: Department of Mathematics, Institute for Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 København, Denmark
- Sean Sather-Wagstaff
- Affiliation: Department of Mathematics, California State University, Dominguez Hills, 1000 E. Victoria Street, Carson, California 90747
- Address at time of publication: Department of Mathematics, North Dakota State University, 300 Minard Hall, Fargo, North Dakota 58105-5075
- Email: sean.sather-wagstaff@ndsu.edu
- Received by editor(s): June 28, 2006
- Received by editor(s) in revised form: March 28, 2007
- Published electronically: February 28, 2008
- Additional Notes: This research was conducted while the first author had a Steno Stipend from the Danish Research Council.
- Communicated by: Bernd Ulrich
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2303-2312
- MSC (2000): Primary 13B35, 13D07, 13D25, 13D45, 13J10
- DOI: https://doi.org/10.1090/S0002-9939-08-09199-5
- MathSciNet review: 2390496
Dedicated: Dedicated to Lex Remington