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.

中文翻译：

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最大理想的力量和（共）同源性的消失

我们证明了可交换的诺特局部环的最大理想的每个正幂都是 Tor 刚体和强刚体。这给出了规律性的新特征，特别是表明，这种理想满足 Huneke 和 Wiegand 长期猜想的扭转条件。