Journal of the
Korean Mathematical Society JKMS

In the current paper we study absolutely pure representations of quivers. Then over some nice quivers including linear quivers some sufficient conditions guaranteeing a representation to be absolutely pure is characterized. Furthermore some relations between flatness and absolute purity is investigated. Finally it is shown that the absolutely pure covering of representations of linear quivers (including $\mathbb{A}_\infty^-$, $\mathbb{A}_\infty^+$ and $\mathbb{A}_\infty^\infty$) by $R$-modules whenever $R$ is a coherent ring exists.

Keywords: representations of a quiver, pure monomorphism, absolutely pure representations, flat representations

MSC numbers: 16G20, 16D90