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Hochschild dimension of a separably generated field


Author: B. L. Osofsky
Journal: Proc. Amer. Math. Soc. 41 (1973), 24-30
MSC: Primary 13C15
DOI: https://doi.org/10.1090/S0002-9939-1973-0318129-9
MathSciNet review: 0318129
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Abstract: Let $ K$ be an $ {\aleph _k}$-generated field extension of the field $ F$ with transcendence degree $ n$. Set $ \operatorname{bidim}(K)$ = the projective dimension of $ K$ as a $ K{ \otimes _F}K$-module. Then $ K$ locally separably generated implies $ \operatorname{bidim}(K) \leqq k + n + 1$, and $ K$ separably generated implies $ \operatorname{bidim}(K) = k + n + 1$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0318129-9
Keywords: Hochschild dimension of fields, bidimensions of fields, cohomology of algebras
Article copyright: © Copyright 1973 American Mathematical Society

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