Abstract
We prove nilpotency of the alternator ideal of a finitely generated binary (-1,1)-algebra. An algebra is a binary (-1,1)-algebra if its every 2-generated subalgebra is an algebra of type (-1,1). While proving the main theorem we obtain various consequences: a prime finitely generated binary (-1,1)-algebra is alternative; the Mikheev radical of an arbitrary binary (-1,1)-algebra coincides with the locally nilpotent radical; a simple binary (-1,1)-algebra is alternative; the radical of a free finitely generated binary (-1,1)-algebra is solvable. Moreover, from the main result we derive nilpotency of the radical of a finitely generated binary (-1,1)-algebra with an essential identity.
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Pchelintsev, S.V. Nilpotency of the Alternator Ideal of a Finitely Generated Binary (-1,1)-Algebra. Siberian Mathematical Journal 45, 356–375 (2004). https://doi.org/10.1023/B:SIMJ.0000021291.69705.6b
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DOI: https://doi.org/10.1023/B:SIMJ.0000021291.69705.6b