Generalized symmetric rings

Kafkas G., ÜNGÖR B., HALICIOĞLU S., Harmanci A.

ALGEBRA & DISCRETE MATHEMATICS, cilt.12, sa.2, ss.72-84, 2011 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 2
  • Basım Tarihi: 2011
  • Dergi Adı: ALGEBRA & DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.72-84
  • Anahtar Kelimeler: symmetric rings, central reduced rings, central symmetric rings, central reversible rings, central semicommutative rings, central Armendariz rings, 2-primal rings, ARMENDARIZ, BAER
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper , we introduce a class of rings which is a generalization of symmetric rings. Let R be a ring with identity. A ring R is called central symmetric if for any a,b,c epsilon R, abc = 0 implies bac belongs to the center of R. Since every symmetric ring is central symmetric, we study sufficient conditions for central of R. Since every symmetric ring is central symmetric, we study sufficient conditions for central symmetric rings for this general setting. We show that every central reversible, central semicommutative, 2-primal, abelian and so directly finite. It is proven that the polynomial ring R[x] is central symmetric if and only if the Laurent polynomial ring R[x, x(-1)] is central symmetric. Among others, it is shown that for a right principally projective ring R, R is central symmetric if and only if R[x]/(x(n)) is central Armendariz, where n >= 2 is a natural number and (x(n)) is the ideal generated by x(n).