关于广义morphic环和伪morphic环的注记

R称为左广义morphic环,若对每个a∈R,存在b,c∈R使得l(a)=Rb,l(b)=Rc。R称为左伪morphic环,若对任意的a∈R,存在b,c∈R使得Ra=l(b),Rb=l(c),其中l(a),l(b),l(c)表示R中元素a,b,c的左零化子。本文主要研究广义morphic环和伪morphic环的部分性质,通过例子说明某些结论的逆命题不成立。反例,设R是环,n≥0,R[x]/(xn+1)是左广义morphic环,则R是左广义morphic环,反之不成立。

Note on Generalized Morphic Rings and Pseudo-morphic Rings

A ring R is called left generalized morphic if for every a∈R,there exist b,c∈R such that l(a)=Rb,l(b)=Rc.A ring R is called left pseudo-morphic if for every a∈R,there exist b,c∈R such that Ra=l(b),Rb=l(c),where l(a),l(b),l(c) denote the left annihilator of a,b,c in R.In this paper,we characterize some properties of generalized morphic rings and pseudo-morphic rings.Also we give some examples for some wrong propositions.For example,if R is a ring,n≥0,R[x]/(xn+1) is left generalized morphic ring,then R left generalized morphic ring.But otherwise it is not established,this article gives the proof.