Document Type : Original Paper
Author
Department of Mathematics, Higher Education center of Eghlid, Eghlid, Islamic Republic of Iran
Abstract
A ring R is said to be right McCoy, if for every f(x),g(x) in the polynomial ring R[x], with f(x)g(x)=0 there exists a nonzero element cϵR with f(x)c=0. In this note, we show that von Neumann regular McCoy rings are abelian. This gives a positive answer to the question rised in Comm. Algebra 42 (2014) 1565- 1570.”
Keywords
- McCoy NH. Remarks on divisors of zero. Amer. Math. Mon. 1942; 49: 286-295.
- Nielsen PP. Semi-commutativity and the McCoy condition. J. Algebra. 2006; 298: 134–141.
- Nasr-Isfahani AR. On semiprime right Goldie McCoy rings. Comm. Algebra. 2014; 42: 1565-1570.
- Lambek J. On the representation of modules by sheaves of factor modules. Canad. Math. Bull. 1971; 14(3): 359-368.
- Mohammadi R, Moussavi A, Zahiri M. On nil-semicommutative rings. Int. Electron. J. Algebra. 2012; 11: 20-37.
- Camillo V, Nielsen PP. McCoy rings and zero-divisors. J. Pure. Appl. Algebra. 2008; 212: 599-615.
- Azimi M, Moussavi A. Nilpotent elements in skew polynomial rings. J. Sci. Islam. Repub. Iran. 2017; 28(1): 59-74.
- Hong CY, Kwak TK. The McCoy condition on skew polynomialrings. Comm. Algebra. 2009; 37 (11): 4026-403.
- Mohammadi R, Zahiri M, Moussavi A. On annihilations of ideals in skew monoid rings. J. Korean. Math. Soc. 2016;53 (2): 381-401.