(untitled) (Communications in Mathematical Research, 2021)
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.