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?.
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