具有对称自同态的环

Rings with Symmetric Endomorphisms

通过引入对称α-环的概念,拓广对称环的研究.讨论对称α-环与相关环的关系,给出对称α-环的一些扩张性质,证明了1)设α是约化环R的自同态且α-1)=1.如果R是对称α-环,则R[x]/〈x^n〉是对称α-环;2)设α是右Ore环R的自同构,Q(R)是R的典范右商环.如果R是对称环,则R是对称α-环当且仅当Q(R)是对称α-环.

In this paper,we extend the study of symmetric rings by introducing the concept of symmetric a-rings.We discuss the relationships between symmetric a-rings and related rings and investigate some extensions of symmetric a-rings.It is shown that l）let a be a endomorphism of a reduced ring R with a（l） = 1.If R is a symmetric a-ring,then R[x]/（x^n）is a symmetric a-ring;2） Let a be a automorphism of a right Ore ring R and Q（R） the classical right quotient ring of R.If R is symmetric,then R is a symmetric a-ring if and only if Q（R）is a symmetric a-ring.