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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An application of the algebra of differentials of infinite rank


Author: William C. Brown
Journal: Proc. Amer. Math. Soc. 35 (1972), 9-15
MSC: Primary 13B10
DOI: https://doi.org/10.1090/S0002-9939-1972-0300999-0
MathSciNet review: 0300999
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Abstract: Let k denote an arbitrary field and let R be an affine local domain over k. Let $ ({\Omega _k}(R),\delta _k^R)$ be the universal algebra of k-higher differentials over R. Let K be the quotient field of R and L the residue class field of R. If K is a separable extension of k and L is a separable algebraic extension of k, then it is shown that R is a regular local ring if and only if $ {\Omega _k}(R)$ is a free R-algebra. If both K and L are separable extensions of k and R has a separating residue class field, then R is a regular local ring if and only if $ {\Omega _k}(R)$ is a free
emphR-algebra.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0300999-0
Keywords: k-higher derivations, algebra of k-higher differentials, separating residue class field, separating representatives
Article copyright: © Copyright 1972 American Mathematical Society