Abstract
Let A be a finitely generated algebra over an absolutely flat commutative ring. Using sheaf-theoretic techniques, it is shown that the weak Hochschild dimension of A is equal to the supremum of the Hochschild dimension of ${A_x}$ for x in the decomposition space of R. Using this fact, relations are obtained among the weak Hochschild dimension of A and the weak global dimensions of A and ${A^e}$. It is also shown that a central separable algebra is a biregular ring which is finitely generated over its center. A result of S. Eilenberg concerning the separability of A modulo its Jacobson radical is extended. Finally, it is shown that every homomorphic image of an algebra of weak Hochschild dimension 1 is a type of triangular matrix algebra.
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