Abstract
In this paper we show that a 2-divisible (-1,1) ring satisfies the identities (x, (y, x, y)) = 0, (x, (y, z), x) = 0, (x, (y, z), w) = ((y, z), w, x) = (w, x, (y, z)). using these identities, we prove that a semiprime 2-divisible (-1,1) ring is isomorphic to a subdirect sum of a semiprime alternative and a semiprime commutative ring. Also, we prove that a prime 2divisible (-1,1) ring R is alternative or commutative.
Keyword
Right alternative rings, (-1,1) Rings, Semiprime rings, Isomorphism, semiprime (-1,1) ring, prime (-1,1) rings.
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