Local rings whose formal fibers are complete intersections
A characterization of smooth and regular algebras in characteristic zero.
On the free character of the first Koszul homology module.
Let (A,M,K) denote a local noetherian ring A with maximal ideal M and residue field K. Let I be an ideal of A and E the Koszul complex generated over A by a system of generators of I. The condition: H1(E) is a free A/I-module, appears in several important results of Commutative Algebra. For instance: - (Gulliksen [3, Proposition 1.4.9]): The ideal I is generated by a regular sequence if and only if I has finite projective dimension and H1...
Some recent results on Hochschild homology of commutative algebras.
This article is a brief survey of the recent results obtained by several authors on Hochschild homology of commutative algebras arising from the second author’s paper [21].
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