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Volume 26, Issue 2
Linearly McCoy Rings and Their Generalizations

Jian Cui & Jianlong Chen

Commun. Math. Res., 26 (2010), pp. 159-175.

Published online: 2021-05

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  • Abstract

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.

  • Keywords

linearly McCoy ring, α-skew linearly McCoy ring, polynomial ring, matrix ring.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{CMR-26-159, author = {Cui , Jian and Chen , Jianlong}, title = {Linearly McCoy Rings and Their Generalizations}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {2}, pages = {159--175}, abstract = {

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} }
TY - JOUR T1 - Linearly McCoy Rings and Their Generalizations AU - Cui , Jian AU - Chen , Jianlong JO - Communications in Mathematical Research VL - 2 SP - 159 EP - 175 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19169.html KW - linearly McCoy ring, α-skew linearly McCoy ring, polynomial ring, matrix ring. AB -

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.

Cui , Jian and Chen , Jianlong. (2021). Linearly McCoy Rings and Their Generalizations. Communications in Mathematical Research . 26 (2). 159-175. doi:
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