Smooth algebras and vanishing of Hochschild homology. (English) Zbl 0726.13008

A homomorphism of commutative rings f: \(A\to B\) yields a \(B\otimes_ AB\)-module structure on B. The author bases on some properties of Hochschild homology and shows that f is regular if A is a Noetherian ring, B a flat Noetherian A-algebra and the flat dimension of B over \(B\otimes_ AB\) is finite. He generalizes his previous result [Manuscr. Math. 59, 491-498 (1987; Zbl 0643.13003)].


13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
13D05 Homological dimension and commutative rings
16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
13E05 Commutative Noetherian rings and modules


Zbl 0643.13003
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