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arXiv · 1704.00191

On $(σ,δ)$-skew McCoy modules

Mohamed Louzari·L'moufadal Benyakoub
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Abstract

Let $(σ,δ)$ be a quasi derivation of a ring $R$ and $M_R$ a right $R$-module. In this paper, we introduce the notion of $(σ,δ)$-skew McCoy modules which extends the notion of McCoy modules and $σ$-skew McCoy modules. This concept can be regarded also as a generalization of $(σ,δ)$-skew Armendariz modules. Some properties of this concept are established and some connections between $(σ,δ)$-skew McCoyness and $(σ,δ)$-compatible reduced modules are examined. Also, we study the property $(σ,δ)$-skew McCoy of some skew triangular matrix extensions $V_n(M,σ)$, for any nonnegative integer $n\geq 2$. As a consequence, we obtain: (1) $M_R$ is $(σ,δ)$-skew McCoy if and only if $M[x]/M[x](x^n)$ is $(\overlineσ,\overlineδ)$-skew McCoy, and (2) $M_R$ is $σ$-skew McCoy if and only if $M[x;σ]/M[x;σ](x^n)$ is $\overlineσ$-skew McCoy.

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Mohamed Louzari, L'moufadal Benyakoub. 2017-04-01. On $(σ,δ)$-skew McCoy modules. https://arxiv.org/abs/1704.00191

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