## Mohamed Louzari

*On McCoy condition and semicommutative rings*

Comment.Math.Univ.Carolin. 54,3 (2013) 329-337.**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

PDF