## The socle series of a Leavitt path algebra

##### Authors
Abrams, Gene
Rangaswamy, Kulumani M.
Molina, Mercedes Siles
##### Description
We investigate the ascending Loewy socle series of Leavitt path algebras $L_K(E)$ for an arbitrary graph $E$ and field $K$. We classify those graphs $E$ for which $L_K(E)=S_{\lambda}$ for some element $S_{\lambda}$ of the Loewy socle series. We then show that for any ordinal $\lambda$ there exists a graph $E$ so that the Loewy length of $L_K(E)$ is $\lambda$. Moreover, $\lambda \leq \omega$ (the first infinite ordinal) if $E$ is a row-finite graph.
Comment: 15 pages
##### Keywords
Mathematics - Rings and Algebras, 16S99, 16D60, 46L89