Morphic代数

Morphic Algebra

给出了morphic代数的定义:代数A称为morphic的是指对于任意自同态α∈End(A)且Aα是A的代数理想时,有A/Aα≌ker(α);给出了morphic代数的一些性质;证明了如下结果:对于任意自同构σ∈End(A),如果自同态σ∈End(A)是morphic的,则ασα也是morphic的,代数A的下列条件等价:(1)A是morphic的,(2)如果A/K≌N,其中K,N是A的理想,则A/N≌K.

An algebra is called morphic,if A/Aα≌ker（α） for all endomorphisms α in End（A） and Aα is a algebra ideal of A. In this paper,we also give some properties of morphic algebra. We show that ：For any isomorphism σ∈End（A）,ασα is morphic in case σ∈End（A）,is morphic; The following are equivalent to an algebra A：（1）A is morphic. （2） If A/K≌N where K and N are ideals of A,then A/N≌K.