Existence of maximal ideals in Leavitt path algebras

Esin S., Kanuni Er M.

TURKISH JOURNAL OF MATHEMATICS, sa.5, ss.2081-2090, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1704-116
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2081-2090
  • İstanbul Kültür Üniversitesi Adresli: Hayır

Özet

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.