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A generalized Jacobian criterion for regularity


Author: Peter Seibt
Journal: Proc. Amer. Math. Soc. 93 (1985), 201-202
MSC: Primary 13D03; Secondary 13H05
DOI: https://doi.org/10.1090/S0002-9939-1985-0770518-2
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.


References [Enhancements On Off] (What's this?)

  • [1] M. André, Homologie des algèbres commutatives, Springer-Verlag, Berlin, Heidelberg and New York, 1974. MR 0352220 (50:4707)
  • [2] M. Barr, A cohomology theory for commutative algebras. I, II, Proc. Amer. Math. Soc. 16 (1965), 1379-1391. MR 0193119 (33:1340)
  • [3] L. Illusie, Complexe cotangent et déformations. I, Lecture Notes in Math., vol. 239, Springer-Verlag, Berlin, Heidelberg and New York, 1971. MR 0491680 (58:10886a)

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Additional Information

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

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