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6

Part of 1985 Iran MO (2nd round)

Problems(1)

Ring - [Iran Second Round 1985]

Source:

12/29/2010
In The ring R\mathbf R, we have ∀x∈R:x2=x\forall x \in \mathbf R : x^2=x. Prove that in this ring
i) Every element is equals to its additive inverse.
ii) This ring has commutative property.
superior algebrasuperior algebra unsolved