McCoy环的扩张(英文)

A ring R is said to be right McCoy if the equation f(x)g(x)=0,where f(x)and g(x)are nonzero polynomials of R[x],implies that there exists nonzero s∈R such that f(x)s=0.It is proven that no proper(triangular)matrix ring is one-sided McCoy.It is shown that for many polynomial extensions,a ring R is right McCoy if and only if the polynomial extension over R is right McCoy.     

关于UR-环

A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and （S, 2）-ring~. Some relations of these rings are studied and several properties of clean rings and （S, 2）-rings are extended. PAng extensions of UR-rings are also investigated.