Rank-one nonincreasing mappings on triangular matrices and some related preserver problems - Chooi, W. L.; Lim, M. H. (2001)
Let T-n(F) be the algebra of all n x n upper triangular matrices over an arbitrary field F. We first characterize those rank-one nonincreasing mappings psi: T-n(F) --> T-m(F), n less than or equal to m such that psi (I-n) is of rank n. We next deduce from this result certain types of singular rank-one r-potent preservers and nonzero r-potent preservers on T-n(F). Characterizations of certain classes of homomorphisms and semi-homomorphisms on T-n(F) are also given.