eprintid: 37244
rev_number: 9
eprint_status: archive
userid: 11647
dir: disk0/00/03/72/44
datestamp: 2020-01-07 06:33:04
lastmod: 2020-01-07 06:33:04
status_changed: 2020-01-07 06:33:04
type: article
metadata_visibility: show
creators_name: Wardati, Khurul
title: ON SEMISIMPLE LEAVITT PATH ALGEBRAS
OVER A COMMUTATIVE UNITAL RING
ispublished: pub
subjects: Matematika
divisions: artkl
full_text_status: public
keywords: ON SEMISIMPLE, LEAVITT PATH ALGEBRAS,
OVER A COMMUTATIVE UNITAL RING
abstract: A finite acyclic graph always contains a sink, a vertex that does not emit edges. Any sink at the graph will generate minimal basic ideal of the Leavitt path algebra over a commutative unital ring. Moreover, the Leavitt path algebra on the finite acyclic graph is a direct sum of minimal basic ideals generated by the sinks. In other words, Leavitt path algebra over the commutative unital ring on the finite acyclic graph is basically semisimple, but not necessarily semisimple. The Leavitt path algebra is semisimple if and only if the commutative unital ring is semisimple.
date: 2017-10-01
date_type: published
publication: JP Journal of Algebra, Number Theory and Applications
volume: 39
number: 5
publisher: Pushpa Publishing House
pagerange: 671-683
refereed: TRUE
issn: 0972-5555
official_url: http://pphmj.com/journals/jpanta.htm
citation:   Wardati, Khurul  (2017) ON SEMISIMPLE LEAVITT PATH ALGEBRAS OVER A COMMUTATIVE UNITAL RING.  JP Journal of Algebra, Number Theory and Applications, 39 (5).  pp. 671-683.  ISSN 0972-5555     
document_url: https://digilib.uin-suka.ac.id/id/eprint/37244/1/JPANTA-2017-SCOPUS-an.Khurul.pdf