On Constant Zero-Divisors of Linear Polynomials

Abstract

Camillo and Nielsen called a ring R right (linearly) McCoy if given nonzero (linear) polynomials f(x), g(x) over R with f(x)g(x) = 0, there exists a nonzero element r ∈ R with f(x)r = 0. Hong et al. called R strongly right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, f(x)r = 0 for some nonzero r in the right ideal of R generated by the coefficients of g(x). We continue the studies of right linearly McCoy and strongly right McCoy rings through finding some nonzero r in various kinds of one-sided ideals of R generated by the coefficients of f(x) or g(x). We investigate interesting relations between newly introduced properties in this note and other standard ring theoretic properties. We provide examples appropriate for the situations occurred naturally in the process.