On a generalization of α-skew McCoy rings

Abstract

Objective: To generalize the -skew McCoy rings. Methods: For a ring endomorphism ‎, ‎‎‎we call a ring Central -skew McCoy if for each pair of nonzero polynomials and satisfy ‎, ‎then there exists a nonzero element with ‎. Findings: ‎For a ring R‎, ‎we show that if for each idempotent ‎, ‎then is Central -skew McCoy if and only if is Central -skew McCoy if and only if‎ is Central -skew McCoy‎. ‎Also‎, ‎we prove that if for some positive integer ‎, is Central -skew McCoy if and only if the polynomial ring is Central -skew McCoy if and only if the Laurent polynomial ring is Central -skew McCoy‎. ‎Moreover‎, ‎we give some examples to show that if is Central -skew McCoy‎, ‎then is not necessary Central -skew McCoy‎, ‎but and are Central -skew McCoy‎, ‎where and are the subrings of the triangular matrices with constant main diagonal and constant main diagonals‎, ‎respectively‎.