[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2013.50.5.1501

Extensions of linearly McCoy rings

Cui, Jian (Department of Mathematics Anhui Normal University)
Chen, Jianlong (Department of Mathematics Southeast University)

Publication Information

Bulletin of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 1501-1511 More about this Journal

Abstract

A ring R is called linearly McCoy if whenever linear polynomials $f(x)$ , $$g(x){\in}R[x$ $]$ ${\backslash}\{0\}$$ satisfy $f(x)g(x)=0$ , there exist nonzero elements $r,s{\in}R$ such that $f(x)r=sg(x)=0$ . In this paper, extension properties of linearly McCoy rings are investigated. We prove that the polynomial ring over a linearly McCoy ring need not be linearly McCoy. It is shown that if there exists the classical right quotient ring Q of a ring R, then R is right linearly McCoy if and only if so is Q. Other basic extensions are also considered.

Keywords

polynomial ring; linearly McCoy ring; matrix ring; semi-commutative ring; McCoy ring;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
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