On a skew McCoy ring

Abstract

A ring R with an endomorphism σ is called σ-skew McCoy, if for any zero-divisor f(x) in the skew polynomial ring R[x; σ], there exists a nonzero element $c\in R$ with f(x)c = 0. In this note, we show that there exists a ring R and an endomorphism σ such that the matrix ring M₂(R) is σ-skew McCoy. This gives a negative answer to the question posed in “A. R. Nasr-Isfahani, On semiprime right Goldie McCoy rings, Commun. Algebra 42 (2014) 1565-1570”.

Keywords:

• McCoy rings
• skew polynomial rings

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• Primary 16S36
• Secondary 16U80
• 16U20