OPERATORS ON REGULAR RINGS OF LEAVITT PATH ALGEBRAS

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Atıf İçin Kopyala

ÖZDİN T.

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
• 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.