POWERS OF THE MAXIMAL IDEAL AND VANISHING OF (CO)HOMOLOGY
AbstractWe 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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2016 ◽
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