Journal of the
Korean Mathematical Society JKMS

Nielsen and Rege-Chhawchharia called a ring $R$ {\it right McCoy} if given nonzero polynomials $f(x), g(x)$ over $R$ with $f(x)g(x)=0$, there exists a nonzero element $r\in R$ with $f(x)r = 0$. Hong et al. called a ring $R$ {\it 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 $g(x)$. Subsequently, Kim et al. observed similar conditions on linear polynomials by finding nonzero $r$'s in various kinds of one-sided ideals generated by coefficients. But almost all results obtained by Kim et al. are concerned with the case of products of linear polynomials. In this paper we examine the nonzero annihilators in the products of general polynomials.

Keywords: right left-ideal-McCoy ring, right McCoy ring, polynomial ring, matrix ring, condition $(\dag)$, Dorroh extension

MSC numbers: 16U80, 16D25, 16S99