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Proceedings of the American Mathematical Society

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

 

 

Abelian extensions of regular local rings


Author: Paul Roberts
Journal: Proc. Amer. Math. Soc. 78 (1980), 307-310
MSC: Primary 13H05; Secondary 13H10
MathSciNet review: 553363
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Abstract: The integral closure of a regular local ring in a finite Abelian extension of its quotient field is Cohen-Macaulay, provided that the degree of the extension is not divisible by the characteristic of the residue field.


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

  • [1] Nicolas Bourbaki, Elements of mathematics. Commutative algebra, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French. MR 0360549
  • [2] Revêtements étales et groupe fondamental, Springer-Verlag, Berlin-New York, 1971 (French). Séminaire de Géométrie Algébrique du Bois Marie 1960–1961 (SGA 1); Dirigé par Alexandre Grothendieck. Augmenté de deux exposés de M. Raynaud; Lecture Notes in Mathematics, Vol. 224. MR 0354651
  • [3] Melvin Hochster, Topics in the homological theory of modules over commutative rings, Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, R.I., 1975. Expository lectures from the CBMS Regional Conference held at the University of Nebraska, Lincoln, Neb., June 24–28, 1974; Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 24. MR 0371879

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0553363-8
Article copyright: © Copyright 1980 American Mathematical Society