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Proceedings of the American Mathematical Society

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

 

 

Free derivation modules and a criterion for regularity


Author: Selmer Moen
Journal: Proc. Amer. Math. Soc. 39 (1973), 221-227
MSC: Primary 13B10
MathSciNet review: 0313239
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Abstract: Let $ k$ be an algebraically closed field of characteristic zero, $ R$ an affine $ k$-algebra. We prove that if the ideal of the variety of $ R$ can be generated by an $ S$-sequence of forms in a polynomial ring $ S$, and if the module of $ k$-derivations of $ R$ into itself is a free $ R$ module, then $ R$ is regular.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0313239-4
Keywords: Regular ring, derivation module, affine algebra, singular prime, Jacobian ideal, projective complete intersection
Article copyright: © Copyright 1973 American Mathematical Society