数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2010年
2期
236-242
,共7页
线性保持%三角矩阵模%交换环
線性保持%三角矩陣模%交換環
선성보지%삼각구진모%교환배
linear preserver%triangular matrix module%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T_n(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.
本文研究瞭交換環上三角矩陣模間的線性保持問題.利用矩陣計算技巧和跼部化技巧,刻畫瞭上三角矩陣T_n(R)上分彆保持立方冪等,{1}逆,{1,2}逆和群逆的所有R模自同構集閤中的元素,其中R是交換環.
본문연구료교환배상삼각구진모간적선성보지문제.이용구진계산기교화국부화기교,각화료상삼각구진T_n(R)상분별보지립방멱등,{1}역,{1,2}역화군역적소유R모자동구집합중적원소,기중R시교환배.
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 T_n (R) that preserve tripotence, {1}-inverse, {1,2}-inverse and group inverse, respectively, when R is a commutative ring.
