1.School of Mathematics and Statistics， Nanjing University of Information Technology， Nanjing 210044， China； 2. School of Information Engineering， Nanjing Xiaozhuang University， Nanjing 211171， China）*-nil McCoy ring(*-诣零McCoy环)

Abstract

We study the properties of McCoy rings with a doubly mapping, give some examples of this class rings, investigate their extensions and the *-nil McCoy property of *-skew polynomial rings. We showed that (1) Let *-ring R satisfy nil(R[x]) = nil(R)[x]. Then R is *-nil McCoy if and only if R[x] is *-nil McCoy; (2) Let R[x; *] be *-skew polynomial ring. If R is *-revisible, then R[x; *] is *-nil McCoy.(研究了具有对合映射*-诣零McCoy环的性质，给出了一批*-诣零McCoy环例子，并讨论了其扩张和*-斜多项式环的*-诣零McCoy性，证明了（1）设*-环R满足nil（R［x］）=nil（R）［x］，则环R是*-诣零McCoy环当且仅当环R［x］是*-诣零McCoy环；（2）设R［x；*］是*-斜多项式环，如果R是*-可逆环，则R［x；*］是*-诣零McCoy环。)

Keywords

• involution(对合)
• mccoy ring(mccoy环)
• *-nil mccoy ring(*-诣零mccoy环)
• *-skew polynomial ring(*-斜多项式环)