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Central ideals of a free finitely generated alternative algebra. (English. Russian original) Zbl 0635.17014
Algebra Logic 25, 296-311 (1986); translation from Algebra Logika 25, No. 4, 470-491 (1986).
Let $$A_ k$$ be a free alternative algebra on k free generators over an associative-commutative ring $$\Phi$$ containing 1/6. Consider the following function (Filippov’s function): $g(y,z,t,v,x)=([[y,z],t,x],x,v)+([[y,x],z,x],t,v),$ where $$[u,v,w]=2(u,v,w)+[u,[v,w]]$$, and next define $\omega_ k(x_ 1,...,x_{k+1})=[... [[g(x_ 1,...,x_ 5),x_ 6],x_ 7],...,x_{k+1}\}.$ It is proved that all the values of the function $$\omega_ k$$ generate a T-ideal $$W(A_ k)$$ in the algebra $$A_ k$$ (k$$\geq 5)$$, which is trivial (i.e. $$W(A_ k)^ 2=0)$$ and lies in the center $$Z(A_ k)$$; at the same time $$W(A_{k+1})\not\subseteq Z(A_{k+1})$$.
Reviewer: I.Shestakov
##### MSC:
 17D05 Alternative rings 17D10 Mal’tsev rings and algebras
Full Text:
##### References:
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