Let πΎ be a field and π be a quiver (directed graph), and let π΄ = πΎπ be the path algebra that corresponds to π with coefficients in πΎ. An π΄-module π is a completely prime (π-prime) module in the sense that ππ = 0 for one π β π and π β π΄ implies that either π annihilates all π or π = 0. In this paper, we prove that for Dynkin quiver type π΄_π and π·_π , an π΄-module π is π-prime if and only if it is simple.
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