| A ring R is called a periodic ring, if for every x∈R there exist two distinct positive integers m(x) and n(x) such that xm(x)=xn(x)(cf. [1]), in particularly, if m(x) = 1 for any x∈R. then this periodic ring is called a Jacobson ring (cf. [2]).In this paper, a necessary and sufficient condition for a ring to be a Jacobson ring is given and some necessary and sufficient conditions for a periodic ring or a Jacobson ring to be a field are also given. |
