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Generalized right alternative rings

Generalized right alternative rings

We show that weakening the hypotheses of right alternative rings to the three identities (1) (ab ,c,d) + (a,b,[c,d]) = a(b,c,d) + (a,c,d)b (2) (α,α,α) = 0 (3) ([a,b],b,b) = O for all α, b, c, d in the ring will not lead to any new simple rings.In fact, the …