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Mat. Zametki, 1976, Volume 19, Issue 2, Pages 291–297 (Mi mz7748)  

The Kleinfeld identities in generalized accessible rings

G. V. Dorofeev

Moscow State Pedagogical Institute

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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English version:
Mathematical Notes, 1976, 19:2, 172–175

Bibliographic databases:

UDC: 519.48
Received: 25.04.1975

Citation: G. V. Dorofeev, “The Kleinfeld identities in generalized accessible rings”, Mat. Zametki, 19:2 (1976), 291–297; Math. Notes, 19:2 (1976), 172–175

Citation in format AMSBIB
\Bibitem{Dor76}
\by G.~V.~Dorofeev
\paper The Kleinfeld identities in generalized accessible rings
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 2
\pages 291--297
\mathnet{http://mi.mathnet.ru/mz7748}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=409571}
\zmath{https://zbmath.org/?q=an:0328.17001|0326.17001}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 2
\pages 172--175
\crossref{https://doi.org/10.1007/BF01098752}


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