On additive transformations preserving a multiplicative matrix function

Let M,(K) be the ring of all n x n matrices over a division ring K, and f be a multiplicative matrix function from M-n(K) to a multiplicative Abelian group with zero G boolean OR {0} (f (AB) = f (A)f (B),for all A, B is an element of M-n(K)). We call an additive transformation phi on M-n(K) preserves a multiplicative matrix function f, if f (phi(A)) = f (A), for all A is an element of M-n(K). In this paper, we characterize all additive surjective transformations on M-n(K) over any division ring K (chK not equal 2) that leave a non-trivial multiplicative matrix function invariant. Applications to several related preservers are considered. (c) 2006 Elsevier Inc. All rights reserved.