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Keywords:
Armendariz rings; McCoy rings; Nagata extension; semicommutative rings; $\sigma$-skew McCoy
Armendariz rings; McCoy rings; Nagata extension; semicommutative rings; $\sigma$-skew McCoy
Summary:
Let $R$ be a ring and $\sigma$ an endomorphism of $R$. We give a generalization of McCoy's Theorem [ Annihilators in polynomial rings, Amer. Math. Monthly 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.
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