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arXiv · 1204.5205

On McCoy Condition and Semicommutative Rings

Mohamed Louzari
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Abstract

Let $R$ be a ring, $σ$ an endomorphism of $R$, $I$ a right ideal in $S=R[x;σ]$ and $M_R$ a right $R$-module. We give a generalization of McCoy's Theorem \cite{mccoy}, by showing that, if $r_S(I)$ is $σ$-stable or $σ$-compatible. Then $\;r_S(I)\neq 0$ implies $r_R(I)\neq 0$. As a consequence, if $R[x;σ]$ is semicommutative then $R$ is $σ$-skew McCoy. Moreover, we show that the Nagata extension $R\oplus_σM_R$ is semicommutative right McCoy when $R$ is a commutative domain.

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Mohamed Louzari. 2012-04-23. On McCoy Condition and Semicommutative Rings. https://arxiv.org/abs/1204.5205

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