Modules witnessing that a Leavitt path algebra is directly infinite

摘要

A ring R is said to be directly infinite when there exists a right R-module B ≠ 0 such that {formula} as a right R-module. In terms of the abelian monoid V(R) of isomorphism classes of finitely generated projective right R-modules, R is directly infinite when there exists a finitely generated projective R-module B ≠ 0 such that [R] = [R] + [B] in V(R). Given a graph E, we completely identify in terms of the graph E all those finitely generated projective right L_K(E)-modules B for which [L_K(E)] = IL_K(E)] + [B] in V(L_K(E)).