Rodicio, Antonio G. Smooth algebras and vanishing of Hochschild homology. (English) Zbl 0726.13008 Comment. Math. Helv. 65, No. 3, 474-477 (1990). 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)]. Reviewer: M.Golasiński (Toruń) Cited in 3 ReviewsCited in 14 Documents MSC: 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 Keywords:regular homomorphism; Hochschild homology; flat dimension Citations:Zbl 0643.13003 × Cite Format Result Cite Review PDF Full Text: DOI EuDML