A GENERALIZATION OF REDUCED RINGS

KÖSE H., ÜNGÖR B., HALICIOĞLU S.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.41, sa.5, ss.689-696, 2012 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 5
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1142/s0219498812500703
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.689-696
  • Anahtar Kelimeler: Reduced rings, Central rigid rings, Central reversible rings, Central semi-commutative rings, Abelian rings, BAER, EXTENSIONS
  • Ankara Üniversitesi Adresli: Evet

Özet

Let R be a ring with identity. We introduce a class of rings which is a generalization of reduced rings. A ring R is called central rigid if for any a, b is an element of R, a(2)b = 0 implies ab belongs to the center of R. Since every reduced ring is central rigid, we study sufficient conditions for central rigid rings to be reduced. We prove that some results of reduced rings can be extended to central rigid rings for this general setting, in particular, it is shown that every reduced ring is central rigid, every central rigid ring is central reversible, central semicommutative, 2-primal, abelian and so directly finite.