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 - <p style="text-align: justify;">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.</p>