Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Algebras over absolutely flat commutative rings

Author: Joseph A. Wehlen
Journal: Trans. Amer. Math. Soc. 196 (1974), 149-160
MSC: Primary 16A16; Secondary 16A60
MathSciNet review: 0345996
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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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Keywords: Hochschild dimension, weak global dimension, idempotents, separable algebra, biregular ring, absolutely flat ring, triangular matrix ring, maximal algebra
Article copyright: © Copyright 1974 American Mathematical Society