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, Volume 59, Issue 4, pp 491–498 | Cite as

Some characterizations of smooth, regular, and complete intersection algebras

  • Antonio G. Rodicio
Article

Abstract

We obtain some characterizations of complete intersection algebras based on the vanishing of André-Quillen (co)homology and the finiteness of the projective dimension of Kähler differentials module. In certain particular cases, we show that\(fd_{B \otimes _A B} \left( B \right)< \infty\) is equivalent to the smoothness of the A-algebra B.

Keywords

Number Theory Algebraic Geometry Topological Group Complete Intersection Projective Dimension 
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References

  1. 1.
    ANDRE, M. Homologie des Algèbres Commutatives. Springer-Verlag: Berlin, Heidelberg, New York (1974)Google Scholar
  2. 2.
    ANDRE, M. Morphismes pseudo-réguliers. To appearGoogle Scholar
  3. 3.
    AVRAMOV, L.L. Homology of local flat extensions and complete intersection defects. Math. Ann. 228 (1977) 27–37Google Scholar
  4. 4.
    AVRAMOV, L.L. Local rings of finite simplicial dimension. Bull. AMS 10 (1984) 289–291Google Scholar
  5. 5.
    BERTHELOT, P., GROTHENDIECK, A., ILLUSIE, L. Théorie des Intersections et Théorème de Riemann-Roch (SGA 6). Lecture Notes in Math. 225. Springer-Verlag (1971)Google Scholar
  6. 6.
    FERRAND, D. Suite régulière et intersection complète. C.R. Acad. Sci. Paris 264 (1967) 427–428Google Scholar
  7. 7.
    GROTHENDIECK, A. Eléménts de Géométrie Algébrique, 0IV Publ. Math. I.H.E.S. 20. Paris (1964)Google Scholar
  8. 8.
    GULLIKSEN, T.H., LEVIN, G. Homology of Local Rings. Queen's Papers in Pure and Appl. Math. Queen's Univ. Kingston, Ontario (1969)Google Scholar
  9. 9.
    ILLUSIE, L. Complexe Cotangent et Déformations, I. Lecture Notes in Math. 239. Springer-Verlag (1971)Google Scholar
  10. 10.
    LICHTENBAUM, S., SCHLESSINGER, M. The cotangent complex of a morphism. Trans. AMS 128 (1967) 41–70Google Scholar
  11. 11.
    QUILLEN, D. On the (co-)homology of commutative rings. Proc. Symp. Pure Math. 17 (1970) 65–87Google Scholar
  12. 12.
    VASCONCELOS, W.V. The complete intersection locus of certain ideals. J. Pure and Appl. Algebra 38 (1985) 367–378Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Antonio G. Rodicio
    • 1
  1. 1.Departamento de AlgebraFacultad de MatemáticasSantiago de CompostelaSpain

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