Abstract
ABmmAcT. Let R be a regular local ring and A an algebra over R which is finitely generated and free as an R-module. Defining the Hochschild dimension of A as R-dirnA left hdA,(A), we show the following: if A modulo its prime radical L(A) is R-free and R-dim A/L(A) -0, then R-dim A left hdA(A/L(A)). Using localization and sheaf theoretic techniques, the result is generalized to regular rings and to absolutely flat (von Neiumann regular) rings. The relationship between the A-homological dimension of the algebra A modulo its prime radical and the algebra modulo its Jacobson radical is explored in view of this result.
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