Powers of the maximal ideal and vanishing of (co)homology

Olgur Celikbas; Ryo Takahashi

doi:10.1017/s0017089519000466

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arXiv · 1901.04108

Powers of the maximal ideal and vanishing of (co)homology

Olgur Celikbas·Ryo 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.

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BibTeX RIS

Olgur Celikbas, Ryo Takahashi. 2019-01-14. Powers of the maximal ideal and vanishing of (co)homology. https://doi.org/10.1017/s0017089519000466

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