A ring R is called left morphic, if for any a ∈ R, there exists b ∈ R such that lR（a） =Rb and lR（b）= Ra. In this paper, we use the method which is different from that of Lee and Zhou to investigate when R[x, σ]...A ring R is called left morphic, if for any a ∈ R, there exists b ∈ R such that lR（a） =Rb and lR（b）= Ra. In this paper, we use the method which is different from that of Lee and Zhou to investigate when R[x, σ]/（x^n） is （left） morphic and when the ideal extension E（R, V） is （left） morphic. It is mainly shown that： （1） If is an automorphism of a division ring R, then S = R[x, σ]/（x^n） （n 〉 1） is a special ring. （2） If d,m are positive integers and n = dm, then E（Zn, mZn） is a morphic ring if and only if gcd（d, m） = 1.展开更多
基金The National Natural Science Foundation （10571026） of China, and the Natural Science Foundation （BK2005207） of Jiangsu Province.
文摘A ring R is called left morphic, if for any a ∈ R, there exists b ∈ R such that lR（a） =Rb and lR（b）= Ra. In this paper, we use the method which is different from that of Lee and Zhou to investigate when R[x, σ]/（x^n） is （left） morphic and when the ideal extension E（R, V） is （left） morphic. It is mainly shown that： （1） If is an automorphism of a division ring R, then S = R[x, σ]/（x^n） （n 〉 1） is a special ring. （2） If d,m are positive integers and n = dm, then E（Zn, mZn） is a morphic ring if and only if gcd（d, m） = 1.
