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(b),l(c)表示R中元素b且c的左零化子.本文主要研究R[D,C]环的伪morphic性,证明了环R[D,C]是左伪morphic的当仅当(1)D是左伪morphic环；(2)对任意的x∈C,存在y∈C使得Cx=lC(y),Dx=lD(y).受文[2]的启发,定义了左[D,C]-伪morphic元,并研究了这类元素的性质.%A ring R is called left pseudomorphic if for every a ∈ R . there exist b,c ∈ R such that Ra = l{b), Rb = l(c), where lib), l(c) denote the left annihilator of b, c in R. In this paper, we characterize the pseudo-morphic properties of R [ D, C ] rings. It is shown that R [ D, C ] is a left pseudo-morphic ring if and only if (1) D is a left pseudo-morphic ring; (2) for any ∈C, there exisst y ∈ C such that Cx = lc(y) and Dx = lD(y). By idea from [2], we define left R[D,C]- pseudo morphic element. Furthermore, we discuss the properties of these elements.
展开▼
