ALGEBRA & DISCRETE MATHEMATICS, vol.12, no.2, pp.72-84, 2011 (ESCI)
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).