Cycles of admissible quivers(in Ukrainian) 

Author 
zelik82@mail.ru
KamenetzPodilsk National University of I. Ohienko

Abstract 
We study cycles of admissible quivers. Some sufficient conditions under which the deletion
of an arrow in the admissible quiver results in another admissible quiver are presented. We also
find a sufficient condition under which the weight of a given cycle in an admissible quiver is
greater than or equal to k.

Keywords 
exponent matrix; admissible quiver; cycle of quiver

Reference 
1. Hazewinkel M., Gubareni N., Kirichenko V.V., Algebras rings and modules, mathematical and its applications,
Springers, 2004, V.1, 380 p.
2. Hazewinkel M., Gubareni N., Kirichenko V.V., Algebras rings and modules, mathematical and its applications, Springers, 2007, V.2, 400 p. 3. Kirichenko V.V., Zelenskiy O.V., Zhuravlev V.N. Exponent matrices and tiled order over discrete valuation rings// International Journal of Algebra and Computation.  2005.  V.15, ¹5&6. – P. 1–16. 4. Zhuravlev V.N. Acceptable quivers// Fundamental and Applied Mathematics. – 2008. – V.14, ¹7. – P. 121–128. (in Russian) 5. Zhuravlev V.N., Zelenskiy A.V., Darmosiuk V.M. Unit quivers of exponent matrices// Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics. – 2012. – ¹4. – P. 27–31. (in Ukrainian) 6. Chernousovs Zh.T., Dokuchaev M.A., Khibina M.A., Kirichenko V.V., Miroshnichenko S.G., Zhuravlev V.N., Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II, Trabalhos do departamento de matematica, Universidade de Sao Paulo, Instituto de matematica e estatistica, Sao PauloBrazil, 2003, 43 p. 
Pages 
38

Volume 
42

Issue 
1

Year 
2014

Journal 
Matematychni Studii

Full text of paper  
Table of content of issue 