周期环的刻划

Characterization of Periodic Rings

证明环 R是周期环的充分必要条件是对 a,b∈ R,均有自然数 m,n,k及常数项为零的整系数多项式 f ( x) ,使得 ambk=anbkf ( b)

The present paper proves that a ring R is a periodic ring if and only if for any a,b∈R, there exist positive integers m,n,k and a polynomial f(x) with integer coefficients and the constant term being zero such that a mb k=a nb kf(b).