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.