Koszul Complexes, Depth and Codepth

Abstract

The notions of Ext-depth and Tor-codepth with respect to an ideal \(\mathfrak {a}\) of a commutative ring R were introduced and investigated by Strooker for R-modules. He also proved (see Strooker (Homological questions in local algebra, Cambridge University Press, Cambridge, 1990)[1, 6.1.6, 6.1.7]) that these can be computed by the use of a Koszul complex when the ideal \(\mathfrak {a}\) is finitely generated.