Primeness of simple modules over path algebras and Leavitt path algebras

Document Type : Original Article


1 Institut Teknologi Bandung

2 Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung 40132, Indonesia.



Let K be a field and E be a directed graph, called quiver in the
following, and let A = KE be the path algebra that corresponds to E with
coefficients in K. An A-module M is a c-prime module in the sense that rm = 0
for one m in M and r in A implies that either r annihilates all M or m = 0. In
this paper, we prove that for any acyclic graph E, an A-module M is c-prime
if and only if it is simple. The primeness of simple modules over Leavitt path
algebras is also discussed. We prove that some classes of simple modules over
Leavitt path algebras, are not c-prime modules.