2007/08/14 by Zhiling Ying, Jianlong Chen, Ying, Zhiling +3
Mathematics · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.0708.1789
A ring R is said to be right McCoy if the equation f(x)g(x)=0, where f(x) and g(x) are nonzero polynomials of R[x], implies that there exists nonzero s ∈ R such that f(x)s = 0. It is proven that no proper (triangular) matrix ring is one-sided McCoy. If there exists the classical right quotient ring Q of a ring R, then R is right McCoy if and only if Q is right McCoy. It is shown that for many polynomial extensions, a ring R is right McCoy if and only if the polynomial extension over R is right McCoy. Other basic extensions of right McCoy rings are also studied.\leftskip0truemm \rightskip0truemm \\it Keywords: matrix ring, McCoy ring, polynomial ring, upper triangular matrix ring.