논문KCI 등재
Projective properties of representations of a quiver of the form Q = •⇉•→•
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We define a projective representation M₁⇉M₂→M₃ of a quiver Q = •⇉•→• and consider their properties. Then we show that any projective representation M₁⇉M₂→M₃ of a quiver Q = •⇉•→• is isomorphic to the quotient of a direct sum of projective representations 0⇉0→P, [수식] and [수식], where e₁(a)=(a,0) and e₂(a)=(0,a).
Abstract
We define a projective representation M₁⇉M₂→M₃ of a quiver Q = •⇉•→• and consider their properties. Then we show that any projective representation M₁⇉M₂→M₃ of a quiver Q = •⇉•→• is isomorphic to the quotient of a direct sum of projective representations 0⇉0→P, [수식] and [수식], where e₁(a)=(a,0) and e₂(a)=(0,a).
참고문헌 (7)
- R. Diestel, "Graph Theory, G.T.M. No.88" (1997), Springer-Verlag
- E. Enochs, "Cyclic quiver rings and polycyclic-by-¯nite group rings", Houston J. Math, 1, pp.1~13 (1999)
- E. Enochs, "A homotopy of quiver morphism with applications to rep-resentations", Canad J. Math., 2(51), pp.294~308 (1999)
- S. Park, "Projective representations of quivers", IJMMS, 2(31), pp.97~101 (2002)
- 박상원, "Injective representations of quivers", 대한수학회논문집, 21(1), pp.37~43 (2006), 대한수학회
- 박상원, "INJECTIVE AND PROJECTIVE PROPERTIES OF REPRESENTATIONS OF QUIVERS WITH n EDGES", 한국수학논문집, 16(3), pp.323~334 (2008), 강원경기수학회
- S. Park, "Injective covers and envelopes of representation of linear quiver", Comm. Algebra, 37(2), pp.515~524 (2009)
관련 논문AI추천
Projective and injective properties of representations of a quiver Q= •→•→•박상원, 한준철강원경기수학회 · 한국수학논문집2009 · 제17권 제3호Projective representations of a quiver with three vertices and two edges as $R[x]$-modules박상원, 한준철강원경기수학회 · 한국수학논문집2012 · 제20권 제3호Projective properties of representations of a quiver Q= ● → ● as R[x]-modules강정희, 박상원, 한준철강원경기수학회 · 한국수학논문집2010 · 제18권 제3호INJECTIVE AND PROJECTIVE PROPERTIES OF REPRESENTATIONS OF QUIVERS WITH n EDGES박상원강원경기수학회 · 한국수학논문집2008 · 제16권 제3호Hereditary and semihereditary representations of quiversAdnane Roudi, Driss Bennis대한수학회 · 대한수학회보2021 · 제58권 제6호Pure injective representations of quiversEsmaeil Hosseini대한수학회 · 대한수학회보2013 · 제50권 제2호
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