We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Existence of maximal ideals in Leavitt path algebras.
- Authors
ESİN, Songül; KANUNİ ER, Müge
- Abstract
Let E be an arbitrary directed graph and let L be the Leavitt path algebra of the graph E over a field K. The necessary and sufficient conditions are given to assure the existence of a maximal ideal in L and also the necessary and sufficient conditions on the graph that assure that every ideal is contained in a maximal ideal are given. It is shown that if a maximal ideal M of L is nongraded, then the largest graded ideal in M, namely gr(M), is also maximal among the graded ideals of L. Moreover, if L has a unique maximal ideal M, then M must be a graded ideal. The necessary and sufficient conditions on the graph for which every maximal ideal is graded are discussed.
- Subjects
GRAPH theory; MAXIMAL ideals; ARBITRARY constants; MATHEMATICAL analysis; MATHEMATICAL models
- Publication
Turkish Journal of Mathematics, 2018, Vol 42, Issue 5, p2081
- ISSN
1300-0098
- Publication type
Article
- DOI
10.3906/mat-1704-116