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Prove that the only idempotent element in a field are 0 and 1
prove that the only idempotent element in a field are 0 and 1
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Priyadarshan Choursiya![best-answer]()
Let a be an idempotent element in a field. Then a^2 = a, so a^2 − a = 0 which implies that a(a − 1) = 0. Since a field has no zero divisors either a = 0 or or a = 1. Hence, the idempotent elements of a division ring are exactly 0 and 1.