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POWERS OF THE MAXIMAL IDEAL AND VANISHING OF (CO)HOMOLOGY

Part of: Local rings and semilocal rings Theory of modules and ideals Commutative algebra: Homological methods

Published online by Cambridge University Press:  10 January 2020

OLGUR CELIKBAS  and
RYO TAKAHASHI
OLGUR CELIKBAS
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA e-mail: olgur.celikbas@math.wvu.edu
RYO TAKAHASHI
Affiliation:
Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Aichi 464-8602, Japan Department of Mathematics, University of Kansas, Lawrence, KS 66045-7594, USA e-mail: takahashi@math.nagoya-u.ac.jp; https://www.math.nagoya-u.ac.jp/~takahashi/
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Abstract

We prove that each positive power of the maximal ideal of a commutative Noetherian local ring is Tor-rigid and strongly rigid. This gives new characterizations of regularity and, in particular, shows that such ideals satisfy the torsion condition of a long-standing conjecture of Huneke and Wiegand.

MSC classification

Primary: 13D07: Homological functors on modules (Tor, Ext, etc.)
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 13D05: Homological dimension 13C12: Torsion modules and ideals

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 1 , January 2021 , pp. 1 - 5
Copyright
© Glasgow Mathematical Journal Trust 2020

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References

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