Year: 2010
Author: Jian Cui, Jianlong Chen
Communications in Mathematical Research , Vol. 26 (2010), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-CMR-19169
Communications in Mathematical Research , Vol. 26 (2010), Iss. 2 : pp. 159–175
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: linearly McCoy ring α-skew linearly McCoy ring polynomial ring matrix ring.