A Class of Abelian Rings

HALICIOĞLU S., Harmanci A., ÜNGÖR B.

BOLETIN DE MATEMATICAS, cilt.25, sa.1, ss.27-37, 2018 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 1
  • Basım Tarihi: 2018
  • Dergi Adı: BOLETIN DE MATEMATICAS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Academic Search Premier, Fuente Academica Plus, zbMATH, DIALNET
  • Sayfa Sayıları: ss.27-37
  • Anahtar Kelimeler: Abelian ring, J-abelian ring, ring extension, EXCHANGE RINGS
  • Ankara Üniversitesi Adresli: Evet

Özet

Let R be a ring with identity and J(R) denote the Jacobson radical of R. A ring R is called J-abelian if ae-ea is an element of J(R) for any a is an element of R and any idempotent e in R. In this paper, many characterizations of J-abelian rings are given. We prove that every J-Armendariz ring is J-abelian. We show that the class of J-abelian rings lies strictly between the class of abelian rings and the class of directly finite rings.