Linear Maps Preserving Tripotence Frome Symmetric Matrix Modules Onto Matrix Modules Over Principal Ideal Domains

Let R be a commutative principal ideal domain with 2,3,5 as units and let n and m be positive integers with n≤m.Suppose f is a linear map from n×nsymmetric matrix modules Sn(R) to m x m matrix modules Mm(R) over R, if X is a tripotent matrix in Sn(R),and f3(X)=f(X),then we say f is a linear tripotence preserver.In this article, we describe the linear maps preserving tripotence of matrices from Sn(R) onto Mm(R).