环上矩阵的群逆与Drazin逆Group Inverses and Drazin Inverses of Matrices over Rings
陈建龙
摘要(Abstract):
本文给出了环上一类方阵有群逆与 Drazin 逆的充要条件及其它们的显式,且此类方阵概括了左右主理想整环上所有方阵。
关键词(KeyWords): 群逆;Drazin逆;高矩阵
基金项目(Foundation):
作者(Author): 陈建龙
参考文献(References):
- 1 Ben-Israel A.Generalized inverses of matrices:a perspective of the work of Penrose.Math Camb Phil Soc,1986;100:407~425
- 2 Drazin M P.Pseudo-inverses in associative rings and semigroups.Amer Math Monthly,1958;65:506~513
- 3 Cline R E.Inverses of rank invariant powers of a matrix.SIAM J Numer Anal,1968;5:182~197
- 4 Robert P.On the group-inverse of a linear transformation.J Math Anal Appl,1968;22:658~669
- 5 庄瓦金.体上GP矩阵的刻划.新疆大学学报,1989;6(4) :24~27
- 6 谢邦杰.抽象代数学.上海科学技术出版社,1982
- 7 Hartwig R E.Block generalized inverses.Arch Rat Mech Anal,1976;61:197~251
- 8 Jacobson N.The Theory of Rings.Amer Math Soc Providence.1943
- 9 庄瓦金.任意体上矩阵的对合函数与广义逆.东北数学,1987;3(1) :57~66
- 10 Rotman J J.An Introduction to Homological Algebra.Academic Press New York,1979
- 11 周土潘.Fitting环的结构.新疆大学学报,1988;5(4) :14~19