Preserver Problems On Matrix Space

In this thesis,we studied the problem of preservnig inverse of matrix algebras over some commutative rings, The main results obtained are as follows:1:In chaper l,we introduced the origin of preserver problems on matrix space and introduced the development of upper triangular matrix space and symmetric space in detail.2:In chaper 2,we characterized maps preserving inverse of matrix on the upper trian-gular matrix algebra over connected commutative rings.3:In chaper 3,we described module homomorphism which preserves inverse of matrix from symmetrix matrix space to matrix algebras over local rings.