Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

On openness of $ H\sb{n}$-locus and semicontinuity of $ n$th deviation


Author: Alfio Ragusa
Journal: Proc. Amer. Math. Soc. 80 (1980), 201-209
MSC: Primary 13D03; Secondary 13H10
DOI: https://doi.org/10.1090/S0002-9939-1980-0577744-1
MathSciNet review: 577744
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: M. André has used the property $ {H_n}$, namely the vanishing of certain homology groups, and the deviation $ {\delta _n}$ to characterize some classes of rings. In the present paper the author establishes an inequality on the deviations and obtains a Nagata criterion for $ {H_n}$-locus and its openness for quotients of complete intersection rings and excellent rings. The upper-semicontinuity for $ {\delta _n}$ is also proved for the same classes of rings.


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

  • [A$ _{1}$] M. André, Homologie des algèbres commutatives, Die Grundlehren der math. Wissenschaften, vol. 206, Springer-Verlag, Berlin and New York, 1974. MR 0352220 (50:4707)
  • [A$ _{2}$] -, Méthode simpliciale en algèbre homologique et algèbre commutative, Lecture Notes in Math., vol. 32, Springer-Verlag, Berlin and New York, 1967. MR 0214644 (35:5493)
  • [Av] L. L. Avramov, Flat morphisms of complete intersection. Dokl. Akad. Nauk SSSR 225 (1975) = Soviet Math. Dokl. 16 (1975). MR 0396558 (53:421)
  • [B] N. Bourbaki, Algèbre commutative, Chapters I-IV, Hermann, Paris, 1961. MR 0171800 (30:2027)
  • [G-L] T. Gulliksen and G. Levin, Homology of local rings, Queen's Papers in Pure and Appl. Math., No. 20, Kingston, Ontario, 1969. MR 0262227 (41:6837)
  • [G-M] S. Greco and M. G. Marinari, Nagata's criterion and openness of loci for Gorenstein and complete intersection (preprint).
  • [K] E. Kunz, Almost complete intersections are not Gorenstein rings, J. Algebra 28 (1974), 111-116. MR 0330158 (48:8496)
  • [M] H. Matsumura, Commutative algebra, Benjamin, New York, 1970. MR 0266911 (42:1813)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13D03, 13H10

Retrieve articles in all journals with MSC: 13D03, 13H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0577744-1
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society