Rings in which every left zero-divisor is also a right zero-divisor and conversely

Ghashghaei E., Kosan M. T., Namdari M., Yildirim T.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.18, sa.5, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 5
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1142/s0219498819500968
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Eversible rings, directly finite, reversible ring, zero-divisor
  • Gazi Üniversitesi Adresli: Evet

Özet

A ring R is called eversible if every left zero-divisor in R is also a right zero-divisor and conversely. This class of rings is a natural generalization of reversible rings. It is shown that every eversible ring is directly finite, and a von Neumann regular ring is directly finite if and only if it is eversible. We give several examples of some important classes of rings (such as local, abelian) that are not eversible. We prove that R is eversible if and only if its upper triangular matrix ring T-n(R) is eversible, and if M-n(R) is eversible then R is eversible.