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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalized Jacobian criterion for regularity


Author: Peter Seibt
Journal: Proc. Amer. Math. Soc. 93 (1985), 201-202
MSC: Primary 13D03; Secondary 13H05
MathSciNet review: 770518
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Abstract: For a commutative noetherian algebra $ B$ over a perfect field $ A$ regularity is equivalent to the flatness of $ {\Omega _{B\vert A}}$ plus $ {H_1}(A,B,B) = 0$ (simplicial homology). In characteristic 0 the homological condition is superfluous.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0770518-2
PII: S 0002-9939(1985)0770518-2
Keywords: Regular local ring, differentials, simplicial (co)homology
Article copyright: © Copyright 1985 American Mathematical Society