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Commutative augmented algebras with two vanishing homology modules. (English) Zbl 0830.13011

The author proves: Let \(A\) be a ring and \(B\) a Noetherian augmented \(A\)- algebra with augmentation ideal \(I\). If \(\text{Tor}^B_i (A,A) = 0 = \text{Tor}^B_j (A,A)\) for some positive even integer \(i\) and some positive odd integer \(j\), then \(I\) is locally generated by a regular sequence.
Reviewer: L.Bican (Praha)

MSC:

13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
13C05 Structure, classification theorems for modules and ideals in commutative rings
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