Completely Prime Modules for Graded Simple Modules Which is Simple Over Leavitt Path Algebra

Abstract

We characterize a graded simple module  in the setting Leavitt path algebras L which is the completely prime module. Let m  M  and r  A, an A-module M is called a completely prime module if    for one m  M  and r  A then 0  or m = 0. In this article, we show that If u is a sink or an infinite emitter, then a graded simple module which is simple  is not a completely prime module.