Semicommutativity of Rings by the Way of Idempotents

Creative Commons License

KÖSE H., ÜNGÖR B., Harmanci A.

FILOMAT, cilt.33, sa.11, ss.3497-3508, 2019 (SCI-Expanded) identifier identifier

  • 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
  • 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.