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초록· 키워드
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We define injective and projective representations of a quiver Q= •→•→•. Then we show that
a representation [수식] of a quiver Q= •→•→• is projective if and only if each M₁, M₂, M ₃is
projective left R-module and f₁(M₁) is a summand of
M₂and f₂(M₂) is a summand of M₃. And we show that
a representation [수식] of a quiver
Q= •→•→•
is injective if and only if each
M₁,M₂,M₃
is
injective left R-module and ker(f₁) is a summand of M₁ and
ker(f₂) is a summand of M₂.
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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-?nite group rings / Houston J. Math. 25 (1) : 1 ~ 13
R. Diestel / 1997 / Graph Theory, G.T.M. No. 88 / Springer-Verlag
R. S. Pierce / 1982 / Associative Algebras, G.T.M. No. 173 / Springer-Verlag
S. Park / 2002 / Projective representations of quivers / IJMMS 31 (2) : 97 ~ 101
E. Enochs / 1999 / Cyclic quiver rings and polycyclic-by-?nite group rings / Houston J. Math. 25 (1) : 1 ~ 13
R. Diestel / 1997 / Graph Theory, G.T.M. No. 88 / Springer-Verlag
R. S. Pierce / 1982 / Associative Algebras, G.T.M. No. 173 / Springer-Verlag
S. Park / 2002 / Projective representations of quivers / IJMMS 31 (2) : 97 ~ 101
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