M-COMMUTING MAPS ON TRIANGULAR AND STRICTLY TRIANGULAR INFINITE MATRICES

Let N-infinity(F) be the ring of infinite strictly upper triangular matrices with entries in an infinite field. The description of the commuting maps defined on N-infinity(F), i.e. the maps f: N-infinity(F) -> N-infinity(F) such that [f(X), X] = 0 for every X is an element of N-infinity(F), is presented. With the use of this result, the form of m-commuting maps defined on T-infinity(F) - the ring of infinite upper triangular matrices, i.e. the maps f: T-infinity(F) -> T-infinity(F) such that [f(X), X-m] = 0 for every X is an element of T-infinity(F), is found.