A generalization of reduced rings

Kose 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: Differential polynomial ring, Jacobson radical, prime radical, 2-primal ring, Baer ring, Armendariz ring, SKEW POLYNOMIAL-RINGS, QUASI-BAER RINGS, ARMENDARIZ RINGS, ORE EXTENSIONS, 2-PRIMAL RINGS, IDEALS, NEED
  • 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 ∈ R, a2b = 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.