两类特殊的三阶矩阵环的Morphic性质(英文)

The Left Morphic Property of Two Special Classes of the 3×3 Matrices

研究了两类特殊三阶矩阵环的左Morphic性质.具体地,设R是环,令L(R)=a11 0 0a21 a22 a230 0 a33|a11,a21,a22,a23,a33∈R和O(R)=a 0 0a21 a a230 0a|a,a21,a23∈R.证得:(1)L(R)和O(R)都不是左Morphic的;(2)当R是唯一Morphic环且R∝R是左Morphic的,O(R)中主对角线为非零元的元素是左Morphic元.

This paper studies the left morphic property of two special classes of 3×3 matrices.Exactly,let R be a ring,set L（R）=a1100 a21a22a23 00a33｜a11,a21,a22,a23,a33∈R and O（R）=a00 a21aa23 00a｜a,a21,a23∈R.It’s shown that（1） Neither L（R） nor O（R） is left morphic;（2） Let R be a uniquely morphic ring and R∝R be a left morphic ring.Then the elements whose principal diagonal are nonzero in R are left morphic in O（R）.