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In this paper we extend the projective properties of representations of a quiver Q= ● → ● as left R-modules to the projective properties of representations of quiver Q= ● → ● as left R[x]-modules. We show that if P is a projective left R-module then 0 → P[x] is a projective representation of a quiver Q = ● → ●as R[x]-modules. And we show 0 → L is a projective representation of Q = ● → ● as R-module if and only if 0 → L[x] is a projective representation of a quiver Q = ● → ● as R[x]-modules. Then we show if P is a projective left R-module then P[x] →id P[x] is a projective representation of a quiver Q ● → ● as R[x]-modules. We also show that if L →id L is a projective representation of Q = ● → ● as R-module, then L[x]→id L[x] is a projective representation of a quiver Q =● → ● as R[x]-modules.
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참고문헌 (8)
참고문헌 신청
E. Enochs / 1999 / A homotopy of quiver morphism with applications to rep-resentations / Canad. J. Math. 51 (2) : 294 ~ 308
E. Enochs / 1999 / Cyclic quiver rings and polycyclic-by-finite group rings / Houston J. Math. 25 (1) : 1 ~ 13
J. Rotman / 1979 / An Introduction to Homological Algebra / Academic Press Inc.
R. Diestel / 1997 / Graph Theory, G.T.M. No.88 / Springer-Verlag
S. Park / 2002 / Projective representations of quivers / Int. J. Math. Math. Sci. 31 (2) : 97 ~ 101
E. Enochs / 1999 / Cyclic quiver rings and polycyclic-by-finite group rings / Houston J. Math. 25 (1) : 1 ~ 13
J. Rotman / 1979 / An Introduction to Homological Algebra / Academic Press Inc.
R. Diestel / 1997 / Graph Theory, G.T.M. No.88 / Springer-Verlag
S. Park / 2002 / Projective representations of quivers / Int. J. Math. Math. Sci. 31 (2) : 97 ~ 101
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