k-Potence preserving maps without the linearity and surjectivity assumptions

Idempotence-preserving maps without the

Idempotence-preserving maps without the linearity and surjectivity assumptions

✍ Xian Zhang 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 237 KB

Let M n (F) be the space of all n × n matrices over a field F of characteristic not 2, and let P n (F) be the subset of M n (F) consisting of all n × n idempotent matrices. We denote by n (F) the set of all maps from M n (F) to itself satisfying A -λB ∈ P n (F) if and only if φ(A)λφ(B) ∈ P n (F) for