PURE INJECTIVE REPRESENTATIONS OF QUIVERS

Title & Authors
PURE INJECTIVE REPRESENTATIONS OF QUIVERS
Hosseini, Esmaeil;

Abstract
Let R be a ring and $\small{\mathcal{Q}}$ 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 $\small{\mathcal{Q}}$ by R-modules is preenveloping. In case $\small{\mathcal{Q}}$ is a left rooted semi-co-barren quiver and R is left Noetherian, we show that every cotorsion flat representation of $\small{\mathcal{Q}}$ is pure injective. If, furthermore, R is $\small{n}$-perfect and $\small{\mathcal{F}}$ is a flat representation $\small{\mathcal{Q}}$, then the pure injective dimension of $\small{\mathcal{F}}$ is at most $\small{n}$.
Keywords
representation of quiver;pure monomorphism;pure injective representation;cotorsion representation;flat representation;pure injective resolution;
Language
English
Cited by
1.
ABSOLUTELY PURE REPRESENTATIONS OF QUIVERS,;;

대한수학회지, 2014. vol.51. 6, pp.1177-1187
1.
ABSOLUTELY PURE REPRESENTATIONS OF QUIVERS, Journal of the Korean Mathematical Society, 2014, 51, 6, 1177
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