FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 3, PAGES 9-53

**Rational operators of the space of formal series**

N. I. Dubrovin

Abstract

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

Location: http://mech.math.msu.su/~fpm/eng/k06/k063/k06302h.htm

Last modified: July 22, 2006