Abstract:Let $R$ be a ring and $\sigma$ an endomorphism of $R$. We give a generalization of McCoy's Theorem [{\it Annihilators in polynomial rings\/}, Amer. Math. Monthly {\bf 64} (1957), 28--29] to the setting of skew polynomial rings of the form $R[x;\sigma]$. As a consequence, we will show some results on semicommutative and $\sigma$-skew McCoy rings. Also, several relations among McCoyness, Nagata extensions and Armendariz rings and modules are studied.
Keywords: Armendariz rings; McCoy rings; Nagata extension; semicommutative rings; $\sigma$-skew McCoy
AMS Subject Classification: 16S36 16U80