*-诣零McCoy环

*-nil McCoy ring

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。

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.