中文摘要：

假设R是一个有单位元1的结合环.探讨了R上分块矩阵Moore-Penrose逆的存在性,得到了环上分块矩阵的Moore-Penrose逆存在性的充要条件.进而,在EBF=0条件下,其中E=I-CC-＋和F=I-A-＋A,给出了Moore-Penrose逆的表达式M=[0 A C B].此结果推广了Pedro Patricio关于友矩阵M=[0 a In b]的Moore-Penrose逆表达式.作为应用,给出一些例子验证了所得到的结果.

英文摘要：

Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices overR is investigated and the sufficient ad necessary conditions for such existence are obtained. Furthermore, the representation of the Moore-Penrose inverse of M=[0 A C B]is given under the condition of EBF - 0, where E - I - CCT and F - I -AfA. This result generalizes the representation of the Moore-Penrose inverse of the companion matrix M =[0 a In b]due to Pedro Patricio. As for applications, some examples are given to illustrate the obtained results.