Admissible quiver, derived from $$$m$$$ pairwise non-equivalent exponent matrices

O.V. Zelenskiy; V.M. Darmosiuk

doi:10.15421/241606

Admissible quiver, derived from $$$m$$$ pairwise non-equivalent exponent matrices

O.V. Zelenskiy (Kamyanets-Podilsky Ivan Ohienko National University)
V.M. Darmosiuk (Mykolaiv National University named after V.O. Sukhomlynskyi)

Abstract

This paper investigates the quivers derived from finite number of exponent matrices. The authors have proved that for any natural m, there is a quiver which is derived from m pairwise non-equivalent exponent matrices.

Keywords

exponent matrix; admissible quiver of exponent matrix; rigid quiver

Full Text:

PDF (Українська)

References

Hazewinkel M., Gubareni N., Kirichenko V.V. Algebras Rings and Modules, 2004; Vol. 1: 380 p.

Hazewinkel M., Gubareni N., Kirichenko V.V. Algebras Rings and Modules, 2007; Vol. 2: 400 p.

Kirichenko V.V., Zelenskiy O.V., Zhuravlev V.N. "Exponent Matrices and Tiled Order over Discrete Valuation Rings", International J. of Algebra and Computation, 2005; 15(5-6): pp. 1-16. doi:10.1142/S0218196705002724

Zelenskiy O.V. "Rigid quivers of joined exponent matrices", Visnyk Kyiv. un-tu. Seriya: fiz.-mat. nauky, 2007; 3: pp. 27-31. (in Ukrainian)

Zhuravlev V.N. "Admissible quivers", Fundament. i priklad. matematika, 2008; 14(7): pp. 121-128. (in Russian)

Zhuravlev V.N., Zelenskiy O.V., Darmosiuk V.M. "Unit quivers of exponent matrix", Visnyk Kyiv. un-tu. Seriya: fiz.-mat. nauky, 2012; 4: pp. 27-31. (in Ukrainian)

Kirichenko V.V., Zhuravlev V.N., Tsyganovskaya I.N. "On rigid quivers", Fundament. i priklad. matematika, 2006; 12(8): pp. 105-120. (in Russian) doi:10.1007/s10958-008-9060-0