交换环上三角矩阵模间的线性保持映射(英文)

LINEAR PRESERVERS BETWEEN TRIANGULAR MATRIX MODULES OVER COMMUTATIVE RINGS

本文研究了交换环上三角矩阵模间的线性保持问题.利用矩阵计算技巧和局部化技巧,刻画了上三角矩阵Tn(R)上分别保持立方幂等,{1}逆,{1,2}逆和群逆的所有R模自同构集合中的元素,其中R是交换环.

This article investigates some linear preserver problems between triangular matrix modules over commutative rings. By using matrix computational techniques and localization techniques, we characterize the elements in the sets of all R-module automorphisms on upper triangular matrix Tn（R） that preserve tripotence, {1}-inverse, {1,2}-inverse and group inverse, re- spectively, when R is a commutative ring.