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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A van Kampen theorem for separable algebras
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by Andy R. Magid PDF
Proc. Amer. Math. Soc. 39 (1973), 483-488 Request permission

Abstract:

If the commutative ring $S$ is the fibre product of ${R_1}$ and ${R_2}$ over $R$, and if ${R_2}$ maps onto $R$, then the fundamental group of $S$ is the profinite free product of the fundamental groups of ${R_1}$ and ${R_2}$ with the fundamental group of $R$ amalgamated.
References
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  • L. N. Childs, On covering spaces and Galois extensions, Pacific J. Math. 37 (1971), 29–33. MR 303493
  • —, Mayer-Vietoris sequences and Brauer groups of nonnormal domains, J. Algebra (to appear).
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  • André Gramain, Topologie des surfaces, Collection SUP: “Le Mathématicien”, vol. 7, Presses Universitaires de France, Paris, 1971 (French). MR 0292094
  • Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215
  • John Milnor, Introduction to algebraic $K$-theory, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. MR 0349811
  • J. P. Murre, Lectures on an introduction to Grothendieck’s theory of the fundamental group, Tata Institute of Fundamental Research Lectures on Mathematics, No. 40, Tata Institute of Fundamental Research, Bombay, 1967. Notes by S. Anantharaman. MR 0302650
  • E. van Kampen, On the connection between the fundamental groups of some related spaces, Amer. J. Math. 55 (1933), 261-267.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 39 (1973), 483-488
  • MSC: Primary 13B05
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0313237-0
  • MathSciNet review: 0313237