Linearly McCoy Rings and Their Generalizations  

作　　者：CUI JIAN CHEN JIAN-LONG 

机构地区：[1]Department of Mathematics, Southeast University, Nanjing, 210096

出　　处：《Communications in Mathematical Research》2010年第2期159-175,共17页数学研究通讯（英文版）

基　　金：The NSF (10871042,10971024) of China;the Specialized Research Fund (200802860024) for the Doctoral Program of Higher Education

摘　　要：A ring R is called linearly McCoy if whenever linear polynomials f（x）, g（x） e R[x]／{0） satisfy f（x）g（x） ： O, 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.A ring R is called linearly McCoy if whenever linear polynomials f（x）, g（x） e R[x]／{0） satisfy f（x）g（x） ： O, 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.

关 键 词：linearly McCoy ring a-skew linearly McCoy ring polynomial ring matrix ring 

分 类 号：O153.3[理学—数学] TN911.22[理学—基础数学]