Abstract
Let F be any field and let Tn(F) be the n × n upper triangular matrix space over F. We denote the set of all n × n upper triangular idempotent matrices over F by Pn(F). A map ϕ on Tn(F) is called a preserver of idempotence if ϕ(Pn(F)) ⊂ Pn(F); and a strong preserver of idempotence if ϕ(Pn(F)) = Pn(F). In this paper, we characterize the bijective linear preservers of idempotence on Tn(F). Further, the strong linear preservers of idempotence on Tn(F) are characterized. Mathematics Subject Classifications: 15A04; 15A03
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