Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Rings of continuous functions and the branch set of a covering

Author(s): M. A. Mulero
Journal: Proc. Amer. Math. Soc. 126 (1998), 2183-2189.
MSC (1991): Primary 54C40, 13B10, 54C10
MathSciNet review: 1451822
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Abstract: This paper gives a characterization of the branch set of a finite covering $X\to S$ of a topological space $S$ , by means of finite $C(S)$ -subalgebras $A$ of $C(X)$ that separate points in $X$ and the module $\Omega _{A/C(S)}$ of its Kähler differentials.

References:

1.: M. Atiyah and I. G. Mac-Donald, Introduction to Commutative Algebra, Addison-Wesley, 1969. MR 39:4129
2.: L. Childs, On covering spaces and Galois extensions, Pacific J. Math. 37 (1971), 29-33. MR 46:2630
3.: D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, 1995. MR 97a:13001
4.: R. Engelking, General Topology, Hermann Verlag, 1989. MR 91c:54001
5.: L. Gillman and M. Jerison, Rings of Continuous Functions, Springer Verlag, 1976. MR 53:11352
6.: F. Gómez, The number of generators of the algebra of Kähler differentials, Demonstratio Math. Vol XXIII, N 2 (1990), 375-383. MR 92b:13036
7.: K. R. Goodearl, Local isomorphisms of algebras of continuous functions, Journal of the London Math. Soc. (2) 16 (1977), 348-356. MR 58:2203
8.: L. F. McAuley and E. E. Robinson. Discrete open and closed mappings on generalized continua and Newman's property, Can. J. Math. vol XXXVI, 6 (1984), 1081-1112. MR 86h:54012
9.: H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1986. MR 88h:13001
10.: M. A. Mulero, Revestimientos finitos y álgebras de funciones continuas, Ph. D. Thesis, Universidad de Extremadura, 1992.
11.: M. A. Mulero, Algebraic properties of rings of continuous functions, Fund. Math., 149 (1996), 55-66. MR 97c:16038
12.: M. A. Mulero, Algebraic characterization of finite (branched) coverings, (Preprint).
13.: M. Raynaud, Anneaux Locaux Henséliens. Lecture Note in Mathematics 169. Springer-Verlag (1970). MR 43:3252
14.: J. B. Sancho and M. T. Sancho, Dimension of dense subalgebras of C(X), Proc. of the A.M.S. Vol.105 (2) (1989). MR 89f:54036

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