Linearly McCoy Rings and Their Generalizations

摘要

A ring R is called linearly McCoy if whenever linear polynomials f(x),g(x) ∈R[x]\{0} satisfy f(x)g(x)=0,then there exist nonzero elements r,s∈R such that f(x)r=sg(x)=0.For a ring endomorphism α,we introduced the notion of α-skew linearly McCoy rings by considering the polynomials in the skew polynomial ring R[x;α] in place of the ring R[x].A number of properties of this generalization are established and extension properties of α-skew linearly McCoy rings are given.