Geodesic
On the Commutator Nilpotency Step of Strictly $(-1,1)$-Algebras
Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 764-771.

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We prove that the commutator algebra of the $c$‑homotope of a strictly $(-1,1)$-algebra is nilpotent of step $\le5$, i.e., that $\mathrm{ad}_c(x_1)\dots\mathrm{ad}_c(x_5)=0$; this bound is sharp.
Keywords: strictly $(-1,1)$-algebra, commutator algebra, nilpotency step, right alternative algebra.
Mots-clés : $c$-homotope 
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     author = {S. V. Pchelintsev},
     title = {On the {Commutator} {Nilpotency} {Step} of {Strictly} $(-1,1)${-Algebras}},
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S. V. Pchelintsev. On the Commutator Nilpotency Step of Strictly $(-1,1)$-Algebras. Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 764-771. http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a10/

[1] S. V. Pchelintsev, “Izotopy pervichnykh $(-1,1)$- i iordanovykh algebr”, Algebra i logika, 49:3 (2010), 388–423 | MR | Zbl

[2] K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov, A. I. Shirshov, Koltsa, blizkie k assotsiativnym, Sovremennaya algebra, Nauka, M., 1978 | MR | Zbl

[3] E. Kleinfeld, “Right alternative rings”, Proc. Amer. Math. Soc., 4 (1953), 939–944 | DOI | MR | Zbl

[4] S. V. Pchelintsev, “Svobodnaya $(-1,1)$-algebra s dvumya porozhdayuschimi”, Algebra i logika, 13:4 (1974), 425–449 | MR | Zbl

[5] I. R. Hentzel, “The characterization of $(-1,1)$-rings”, J. Algebra, 30:1-3 (1974), 236–258 | DOI | MR | Zbl

[6] R. E. Roomeldi, “Tsentry svobodnogo $(-1,1)$-koltsa”, Sib. matem. zhurn., 18:4 (1977), 861–876 | MR | Zbl

[7] E. Kleinfeld, “On a class of right alternative rings”, Math. Z., 87:1 (1965), 12–16 | DOI | MR | Zbl