THE McCOY CONDITION ON SKEW POLYNOMIAL RINGS

Based on a theorem of McCoy on commutative rings, Nielsen called a ring R right McCoy if, for any nonzero polynomials f(x), g(x) over R, f(x)g(x) = 0 implies f(x)r = 0 for some 0 not equal r is an element of R. In this note, we consider a skew version of these rings, called sigma-skew McCoy rings, with respect to a ring endomorphism sigma. When sigma is the identity endomorphism, this coincides with the notion of a right McCoy ring. Basic properties of sigma-skew McCoy rings are observed, and some of the known results on right McCoy rings are obtained as corollaries.