International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 2, Pages 97-101
Projective representations of quivers
Department of Mathematics, Dong-A University, Pusan 604-714, Korea
Received 30 August 2001
Copyright © 2002 Sangwon Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove that
is a projective representation of a quiver if and only if and are projective left -modules, is an injection, and is a summand. Then, we generalize the result so that a representation of a quiver is projective representation if and only if each is a projective left -module and the representation is a direct sum of projective representations.