Commutative algebras of finite Hochschild homological dimension (Q1188270)

The main topic of this paper is the characterization of regular homomorphisms of finite flat dimension. Let \(k\) be a subfield of a ring \(A\). The authors obtain a necessary and sufficient condition for the finiteness of the flat dimension of \(A\) as a module over \(A\otimes_ kA\) when \(A\) is a field extension of \(k\) or \(A\) is a Dedekind domain whose residue fields are separable over \(k\).