Semicommutativity of Rings by the Way of Idempotents
FILOMAT, cilt.33, sa.11, ss.3497-3508, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 33 Sayı: 11
- Basım Tarihi: 2019
- Doi Numarası: 10.2298/fil1911497k
- Dergi Adı: FILOMAT
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.3497-3508
- Anahtar Kelimeler: Semicommutative ring, e-semicommutative ring, symmetric ring, e-symmetric ring, idempotent, MODULES
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Ankara Üniversitesi Adresli: Evet
Özet
In this paper, we focus on the semicommutative property of rings via idempotent elements. In this direction, we introduce a class of rings, so-called right e-semicommutative rings. The notion of right e-semicommutative rings generalizes those of semicommutative rings, e-symmetric rings and right e-reduced rings. We present examples of right e-semicommutative rings that are neither semicommutative nor e-symmetric nor right e-reduced. Some extensions of rings such as Dorroh extensions and some subrings of matrix rings are investigated in terms of right e-semicommutativity. We prove that if R is a right e-semicommutative clean ring, then the corner ring eRe is clean.