关于非交换主理想整环上正则矩阵的广义逆

On Generalized Inverses of Regular Matrices over a Non-Comutative Principal ideal Domain

利用Ｊａｃｏｂｓｏｎ相抵化简，本文证得了非交换主理想整环Ｒ上幂等矩阵的相似化简，因而给出了Ｒ上正则矩阵的（２）－逆以及当（１，ｉ，…，ｊ）－逆存在时（２，ｉ，…，ｊ）－逆的显公式，其中｛２，ｉ，…，ｊ｝｛２，３，４｝．

This paper studies the generalized inverses of a von Neumann regular matrix A over a non-comutative principal ideal domain R, gives the explicit formulas of A {2 },A {2,3 },A{2,4)and A {2. 3,4 }, where A {2,..,i}≠Φ.