Gorenstein Algebras and Hochschild Cohomology

摘要

Each one of the main classes of commutative Noetherian rings-regular, complete intersection, Gorenstein, and Cohen-Macaulay-is defined by local properties that require verification at every maximal ideal. It is therefore important to develop for these properties global recognition criteria involving only finitely many invariants. Finitely generated algebras over fields provide the test case. Our goal is to devise finitistic global tests applicable also in a more general, relative situation.