On Endomorphism Rings of Leavitt Path Algebras

Creative Commons License

ÖZDİN T.

FILOMAT, cilt.32, sa.4, ss.1175-1181, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.2298/fil1804175o
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1175-1181
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

Let E be an arbitrary graph, K be any field and A be the endomorphism ring of L := L-K(E) considered as a right L-module. Among the other results, we prove that: (1) if A is a von Neumann regular ring, then A is dependent if and only if for any two paths in L satisfying some conditions are initial of each other, (2) if A is dependent then L-K(E) is morphic, (3) L is morphic and von Neumann regular if and only if L is semisimple and every homogeneous component is artinian.