On a generalization of alternative and Lie rings
Abstract: Alternative as well as Lie rings satisfy all of the following four identities: (i) , (ii) , (iii) , (iv) , where the associator is defined by . If is a ring of characteristic different from two and satisfies (iv) and any two of the first three identities, then it is shown that a necessary and sufficient condition for to be alternative is that whenever are contained in a subring of which can be generated by two elements and whenever , then .
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Keywords: Alternative ring, nonassociative ring, identities, division ring, Artin's theorem, projective plane
Article copyright: © Copyright 1971 American Mathematical Society