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  • Friedrich Wehrung
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Part of the Lecture Notes in Mathematics book series (LNM, volume 2188)

Abstract

Let M be a countable conical refinement monoid and let \(\mathbb{k}\) be a countable field. Is there a countable fundamental Boolean inverse semigroup S such that \(\mathop{\mathrm{Typ}}\nolimits S\cong \mathop{\mathrm{V}}\nolimits (\mathbb{k}\langle S\rangle )\cong M\)?

Bibliography

  1. 3.
    Adámek, J., Rosický, J.: Locally Presentable and Accessible Categories. London Mathematical Society Lecture Note Series, vol. 189. Cambridge University Press, Cambridge (1994). MR 1294136 (95j:18001)Google Scholar
  2. 6.
    Ara, P.: The realization problem for von Neumann regular rings. In: Ring Theory 2007, pp. 21–37. World Scientific Publishing, Hackensack, NJ (2009). MR 2513205 (2010k:16020)Google Scholar
  3. 50.
    Goodearl, K.R.: von Neumann Regular Rings, 2nd edn. Robert E. Krieger Publishing Co., Inc., Malabar, FL (1991). MR 1150975 (93m:16006)Google Scholar
  4. 52.
    Goodearl, K.R., Handelman, D.E.: Tensor products of dimension groups and K 0 of unit-regular rings. Can. J. Math. 38(3), 633–658 (1986). MR 845669 (87i:16043)Google Scholar
  5. 66.
    Kaplansky, I.: Fields and Rings. The University of Chicago Press, Chicago, IL, London (1969). MR 0269449 (42 #4345)Google Scholar
  6. 81.
    McCune, W.: Prover9 and Mace4 [computer software], 2005–2010Google Scholar
  7. 92.
    Passman, D.S.: Infinite Group Rings. Pure and Applied Mathematics, vol. 6. Marcel Dekker, Inc., New York (1971). MR 0314951 (47 #3500)Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  • Friedrich Wehrung
    • 1
  1. 1.Département de MathématiquesUniversité de Caen NormandieCaenFrance

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