An application of the Zhou radical to the e-reversibility of rings
Algebra and Discrete Mathematics, cilt.41, sa.2, ss.281-304, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 41 Sayı: 2
- Basım Tarihi: 2026
- Doi Numarası: 10.12958/adm2462
- Dergi Adı: Algebra and Discrete Mathematics
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.281-304
- Anahtar Kelimeler: and phrases: reversible ring, e-reversible ring, idem-potent element, Morita context, Zhou radical
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Ankara Üniversitesi Adresli: Evet
Özet
Let R be a ring and e be an idempotent element of R. The Zhou radical of R denoted by δ(R) is the intersection of maximal essential right ideals of R. In the literature, e-reversible rings were studied regarding the question of how idempotent elements affect the reversible property of rings. In this paper, we pro-vide an application of the Zhou radical of a ring to the reversibility depending on idempotents. Accordingly, we study rings R in which ab = 0 implies bae ∈ δ(R) (or eba ∈ δ(R)), where a, b ∈ R, called Zhou right (or left) e-reversible rings. Besides studying the structure of Zhou e-reversible rings, we investigate relations between Zhou e-reversible rings and some known rings, such as Zhou e-reduced rings, central reversible rings, NI-rings, semiperfect rings and matrix rings. In addition to these, we determine the Zhou radical of some certain rings, such as Morita context rings and special sub-rings of a direct product of rings.