Hochschild dimension and the prime radical of algebras
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- by Joseph A. Wehlen PDF
- Proc. Amer. Math. Soc. 83 (1981), 443-447 Request permission
Abstract:
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 $R - \dim A = {\text {left}}\;{\text {h}}{{\text {d}}_{{A^e}}}(A)$, we show the following: if A modulo its prime radical $L(A)$ is $R$-free and $R - \dim A/L(A) = 0$, then $R - \dim A = {\text {left}}\;{\text {h}}{{\text {d}}_A}(A/L(A))$. Using localization and sheaf theoretic techniques, the result is generalized to regular rings and to absolutely flat (von Neumann 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.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 443-447
- MSC: Primary 16A62; Secondary 13D05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627665-1
- MathSciNet review: 627665