Title of article :
ON LEAVITT PATH ALGEBRAS OVER COMMUTATIVE RINGS
Author/Authors :
Kanwar, Pramod Department of Mathematics Ohio - University-Zanesville Zanesville, USA , Khatkar, Meenu Department of Mathematics - Indian Institute of Technology Delhi, India , Sharma, R. K. Department of Mathematics - Indian Institute of Technology Delhi, India
Abstract :
In this article, basic ideals in a Leavitt path algebra over a commutative unital ring are studied. It is shown that for a finite acyclic graph E
and a commutative unital ring R, the Leavitt path algebra LR(E) is a direct
sum of minimal basic ideals and that for a commutative ring R and a graph
E satisfying Condition (L), the Leavitt path algebra LR(E) has no non-zero
nilpotent basic ideals. Uniqueness theorems for Leavitt path algebras over
commutative unital rings are also discussed.
Keywords :
Leavitt path algebra , basic ideal , minimal basic ideal , uniqueness theorem
Journal title :
International Electronic Journal of Algebra
