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A ring $R$ is called linearly McCoy if whenever linear polynomials $f(x)$, $g(x) ∈ R[x]$\{0} satisfy $f(x)g(x) = 0$, then there exist nonzero elements $r, s ∈ R$ such that $f(x)r = sg(x) = 0$. For a ring endomorphism $α$, we introduced the notion of $α$-skew linearly McCoy rings by considering the polynomials in the skew polynomial ring $R[x; α]$ in place of the ring $R[x]$. A number of properties of this generalization are established and extension properties of $α$-skew linearly McCoy rings are given.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19169.html} }A ring $R$ is called linearly McCoy if whenever linear polynomials $f(x)$, $g(x) ∈ R[x]$\{0} satisfy $f(x)g(x) = 0$, then there exist nonzero elements $r, s ∈ R$ such that $f(x)r = sg(x) = 0$. For a ring endomorphism $α$, we introduced the notion of $α$-skew linearly McCoy rings by considering the polynomials in the skew polynomial ring $R[x; α]$ in place of the ring $R[x]$. A number of properties of this generalization are established and extension properties of $α$-skew linearly McCoy rings are given.