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 Fundam. Prikl. Mat., 2006, Volume 12, Issue 3, Pages 9–53 (Mi fpm947)

Rational operators of the space of formal series

N. I. Dubrovin

Abstract: The main result of this paper is the following theorem: the group ring of the universal covering $\mathbb G$ of the group $\mathrm{SL}(2,\mathbb R)$ is embeddable in a skew field $\mathbb D$ with valuation in the sense of Mathiak and the valuation ring is an exceptional chain order in the skew field $\mathbb D$, i.e., there exists a prime ideal that is not completely prime. In this ring, every divisorial right fractional ideal is principal, and the linearly ordered set of all divisorial fractional right ideals is isomorphic to the real line. This theorem is a consequence of the fact that the universal covering group $\mathbb G$ satisfies sufficient conditions for the embeddability of the group ring of a left ordered group in a skew field.

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English version:
Journal of Mathematical Sciences (New York), 2008, 149:3, 1191–1223

Bibliographic databases:

UDC: 512.8

Citation: N. I. Dubrovin, “Rational operators of the space of formal series”, Fundam. Prikl. Mat., 12:3 (2006), 9–53; J. Math. Sci., 149:3 (2008), 1191–1223

Citation in format AMSBIB
\Bibitem{Dub06} \by N.~I.~Dubrovin \paper Rational operators of the space of formal series \jour Fundam. Prikl. Mat. \yr 2006 \vol 12 \issue 3 \pages 9--53 \mathnet{http://mi.mathnet.ru/fpm947} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2249705} \zmath{https://zbmath.org/?q=an:1152.16034} \elib{http://elibrary.ru/item.asp?id=9307289} \transl \jour J. Math. Sci. \yr 2008 \vol 149 \issue 3 \pages 1191--1223 \crossref{https://doi.org/10.1007/s10958-008-0059-3} \elib{http://elibrary.ru/item.asp?id=14569760} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-39049111518} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Graeter J., Sperner R.P., “on Embedding Left-Ordered Groups Into Division Rings”, Forum Math., 27:1 (2015), 485–518
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