Abstract:
It is proved that the identities $([x,y]^4,z,t)=([x,y]^2,z,t)[x,y]=[x,y]([x,y]^2,z,t)=0$, known in the theory of alternative rings as the Kleinfeld identities, are fulfilled in every generalized accessible ring of characteristic different from 2 and 3. These identities allow us to construct central and kernel functions in the variety of generalized accessible rings. It is also proved that in a free generalized accessible and a free alternative ring with more than three generators the Kleinfeld element $([x,y]^2,z,t)$ is nilpotent of index 2.
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