THE STUDY OF PROJECTIVE MODULE OVER PATH ALGEBRAS AND LEAVITT PATH ALGEBRAS - K, Delsi
This dissertation deals with two topics, namely projective modules over path algebras and projective modules over Leavitt path algebras. In the first topic, the path algebras of finite, connected, and acyclic graphs are hereditary algebras. Therefore all of the projective modules over path algebras of finite, connected, and acyclic graphs are hereditary modules. The main result of the study of projective modules over path algebra is the characterization of hereditary modules over selfinjective Nakayama algebras of a cycle graph. This result is used to characterize hereditary modules over path algebras of a graph that contains cycles. In the second topic, Leavitt path algebras are hereditary so all of the projective modules are hereditary. Based on the fact that Leavitt path algebras are hereditary modules, i.e., every left ideal of Leavitt path algebra is projective, previous researchers have determined the projective resolution of Chen simple modules over Leavitt path algebras. The main result of the study of projective modules over Leavitt path algebras is the U-projective of Chen simple modules over Leavitt path algebras and the graded simple module over Leavitt path algebras.