Cohomological dimension and global dimension of algebras
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- by Joseph A. Wehlen PDF
- Proc. Amer. Math. Soc. 32 (1972), 75-80 Request permission
Abstract:
Let R be a regular local ring and A an algebra over R which is an R-progenerator. Defining the cohomological dimension of A as $R\text {-}\dim A = {\text {l}} \cdot {\text {hd}_{{A^e}}}(A)$, one obtains the Hochschild cohomological dimension of A as an R-algebra. We show the following under the additional hypothesis that R-dim A is finite: (1) $R\text {-}\dim A = n$ iff $A/N$ is R-separable and ${\text {l}} \cdot {\text {hd}_A}(A/N) = n + {\text {gl}}\;\dim R$; (2) ${\text {gl}}\;\dim A = R{\text {-}}\dim A + {\text {gl}} \dim R$; (3) A is R-separable iff ${\text {gl}}\;\dim {A^e} = {\text {gl}}\;\dim R$.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 75-80
- MSC: Primary 16A60
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291226-1
- MathSciNet review: 0291226