OPERATORS ON REGULAR RINGS OF LEAVITT PATH ALGEBRAS
Bulletin of the Transilvania University of Brasov, Series III: Mathematics and Computer Science, cilt.65, sa.1, ss.171-184, 2023 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 65 Sayı: 1
- Basım Tarihi: 2023
- Doi Numarası: 10.31926/but.mif.2023.3.65.1.13
- Dergi Adı: Bulletin of the Transilvania University of Brasov, Series III: Mathematics and Computer Science
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.171-184
- Anahtar Kelimeler: associated elements, Leavitt path algebra, partial order, shorted operator, unit-regular ring, von Neumann regular ring
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Erzincan Binali Yıldırım Üniversitesi Adresli: Evet
Özet
In [8, Theorem 1], Jain and Prasad obtained a kind of symmetry of regular rings which is interesting and useful in the theory of shorted operators (cf. [9]). We show that this symmetry property indeed holds for endo-morphism rings of Leavitt path algebras. Using this property, we analyze a (strong/weak) regular inverse of an element of the regular the endomorphism ring A of the Leavitt path algebra L:= LK (E) (viewed as a right L-module). We also introduce some partial orders on the endomorphism ring A of the Leavitt path algebra L and investigate the behavior of regular elements in A.