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Free nonassociative supercommutative algebras. (Russian, English) Zbl 1072.17002
Fundam. Prikl. Mat. 9, No. 3, 103-109 (2003); translation in J. Math. Sci., New York 135, No. 5, 3336-3340 (2006).
A free nonassociative supercommutative algebra $$A$$ on the alphabets $$X$$ and $$Y$$ over a field $$F$$ is a factor-algebra of the free nonassociative algebra over $$F$$ on the alphabet $$X\coprod Y$$ on the ideal generated by all identities of type $$uv=-\delta vu$$, here $$\delta=-1$$ if $$u,v$$ are both odd and $$\delta=1$$ otherwise. It is proved that homogeneous subalgebras of free nonassociative supercommutative algebras are free. As a consequence, it is shown that the group of automorphisms of a free nonassociative supercommutative algebras is generated by elementary automorphisms.

##### MSC:
 17A50 Free nonassociative algebras