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A van Kampen theorem for separable algebras


Author: Andy R. Magid
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
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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 [Enhancements On Off] (What's this?)

  • [1] H. Bass, Algebraic $ K$-theory, Benjamin, New York, 1968. MR 40 #2736. MR 0249491 (40:2736)
  • [2] L. Childs, On covering spaces and Galois extensions, Pacific J. Math. 37 (1971), 29-33. MR 0303493 (46:2630)
  • [3] -, Mayer-Vietoris sequences and Brauer groups of nonnormal domains, J. Algebra (to appear).
  • [4] F. DeMeyer and I. Ingraham, Separable algebras over commutative rings, Lecture Notes in Math, vol. 181, Springer-Verlag, New York and Berlin, 1971. MR 43 #6199. MR 0280479 (43:6199)
  • [5] A. Gramain, Topologie des surfaces, Presses universitaires de France, Paris, 1971. MR 0292094 (45:1181)
  • [6] M. Hall, The theory of groups, Macmillan, New York, 1959. MR 21 #1996. MR 0103215 (21:1996)
  • [7] J. Milnor, Introduction to algebraic $ K$-theory, Ann. of Math. Studies 72, Princeton Univ. Press, Princeton, N.J., 1971. MR 0349811 (50:2304)
  • [8] J. Murre, Lectures on an introduction to Grothendieck's theory of the fundamental group, Tata Institute of Fundamental Research, Bombay, 1967. MR 0302650 (46:1794)
  • [9] 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

DOI: https://doi.org/10.1090/S0002-9939-1973-0313237-0
Keywords: Separable algebra, profinite group, fibre product, cartesian square, co-cartesian square, fundamental group
Article copyright: © Copyright 1973 American Mathematical Society

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