FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 3, PAGES 215-223

**Quivers of semi-maximal rings**

S. I. Tsupiy

Abstract

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In this paper, the set of quivers of semi-maximal rings is
investigated.
It is proved that the elements of this set are formed by the elements
of the set of quivers of tiled orders and that the set of quivers of
tiled orders with $n$ vertices is
determined by the integer points of a convex polyhedral domain
that lie in the nonnegative part of the space $$**R**^{n2−n}.
It is also proved that the set of quivers of tiled orders with
$n$ vertices
contains all simple oriented strongly connected graphs with
$n$ vertices
and $n$ loops, does not
contain any graphs with $n$ vertices and
$n$-
1 loops, and contains only a part of the
graphs with $n$ vertices and
$m$ ($m\; <\; n$-
1) loops.

Location: http://mech.math.msu.su/~fpm/eng/k05/k053/k05315h.htm

Last modified: September 14, 2005