Pure injective representations of quivers
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Let R be a ring and Q be a quiver. In this paper we give another definition of purity in the category of quiver representations. Under such definition we prove that the class of all pure injective representations of Q by R-modules is preenveloping. In case Q is a left rooted semi-cobarren quiver and R is left Noetherian, we show that every cotorsion flat representation of Q is pure injective. If, furthermore, R is n-perfect and F is a flat representation Q, then the pure injective dimension of F is at most n.
Abstract
Let R be a ring and Q be a quiver. In this paper we give another definition of purity in the category of quiver representations. Under such definition we prove that the class of all pure injective representations of Q by R-modules is preenveloping. In case Q is a left rooted semi-cobarren quiver and R is left Noetherian, we show that every cotorsion flat representation of Q is pure injective. If, furthermore, R is n-perfect and F is a flat representation Q, then the pure injective dimension of F is at most n.
참고문헌 (13)
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