Generalized Inverse Of Linear Preserver Problems

Let R be a principal ideal domain and Mn(R) denotes the n x n matrix algebras over R. The operator preserving group inverses of matrices on Mn(K), where K is communitive local ring or general communitive ring or division ring and chK 2,3, is characterised in reference [5]. In this paper,as the complementary of reference [5], when ch.fi! = 2, we characterise a linear mapping preserving group inverses of matrices on Mn(R}. It is the same way to characterise the linear mapping preserving {1} inverses of matrices on Mn(R).By using the result of reference [8] ,we characterise the linear mapping preserving inverses of matrices from Mn(R) to Mm(R),where n m, chR 2, and the inverse linear mapping preserving inverses of matrices from Mn(R) to Mn(R) when chR = 2.