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International Journal of Mathematics and Mathematical Sciences
Volume 31, Issue 2, Pages 97-101
http://dx.doi.org/10.1155/S0161171202108192

Projective representations of quivers

Department of Mathematics, Dong-A University, Pusan 604-714, Korea

Received 30 August 2001

Copyright © 2002 Hindawi Publishing Corporation. 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.

Abstract

We prove that P1fP2 is a projective representation of a quiver Q= if and only if P1 and P2 are projective left R-modules, f is an injection, and f(P1)P2 is a summand. Then, we generalize the result so that a representation M1f1M2f2fn2Mn1fn1Mn of a quiver Q= is projective representation if and only if each Mi is a projective left R-module and the representation is a direct sum of projective representations.