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Weak Novikov identity in the join of \((-1,1)\) rings. (English) Zbl 1337.17005

Summary: If \(R\) is a \((-1,1)\) ring of characteristic \(\neq 2,3\) with weak Novikov identity \((w,x,yz) = y(w,x,z)\) then the strong Novikov identity \(x(yz) = y(xz)\) holds good in a prime ring \(R\). With this it is proved that \(R\) is associative.

MSC:

17A30 Nonassociative algebras satisfying other identities
17D20 \((\gamma, \delta)\)-rings, including \((1,-1)\)-rings
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