保矩阵群逆的线性算子

Linear operators in preserving group inverses of matrices

近年来一些作者对线性保持问题给予了极大的关注,但研究在环上保群逆的文章尚很少,文献[5]给出了2是单位的环上矩阵保群逆的线性算子的刻划。补充了[5]的结果,令R是特征2的主理想整环,M_0(R)记R上n×n矩阵代数,刻划了在R上保M_n(R)中矩阵的群逆的线性算子的形式。

In recent years, some authors have given more attention to kinear preserver problem, but the articles on preserving group inverses of matrices over a ring are still scarce. [5] gives a characterization on linear operators presering group inverses of matrices over a ring with 2 is an unit. The study of [5] is also supplemented. Let R be a principal ideal domain with chR = 2 and Mn(R) denotes the n x n matric algebras over R, the forms of linear operators preserving group inverses of matrices in Mn(R) are deterimined.