Geodesic
Primitive Elements of Free Commutative Non-associative Algebras and Free Anti-commutative Non-associative Algebras
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 4, pp. 105-124

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Improved algorithms to construct complements of primitive systems of elements of free commutative and anticommutative non-associative algebras with respect to free generating sets and algorithms to realize the rank of a system of elements are constructed and implemented.
Keywords: free non-associative algebras, free commutative non-associative algebras, free anti-commutative non-associative algebras, primitive elements, rank of a system of elements, automorphisms of free algebras. 
@article{VNGU_2010_10_4_a7,
     author = {A. A. Mikhalev and A. V. Mikhalev and A. A. Chepovskiy},
     title = {Primitive {Elements} of {Free} {Commutative} {Non-associative} {Algebras} and {Free} {Anti-commutative} {Non-associative} {Algebras}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {105--124},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2010_10_4_a7/}
}
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A. A. Mikhalev; A. V. Mikhalev; A. A. Chepovskiy. Primitive Elements of Free Commutative Non-associative Algebras and Free Anti-commutative Non-associative Algebras. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 4, pp. 105-124. http://geodesic.mathdoc.fr/item/VNGU_2010_10_4_a7/