Geodesic
Subalgebras of free algebras of some varieties of multioperator algebras
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 24 (1969) no. 1, pp. 15-24

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The problem whether subalgebras of free algebras of various varieties are free plays an important role in general algebra. For some varieties of linear algebras over a field the problem was solved by Kurosh [1] and Shirshov [2], [3]. Kurosh [4] introduced the concept of multioperator algebra over a field and proved that every subalgebra of a free multioperator algebra is free. This paper is devoted to a study of varieties of multioperator algebras given by identities of a special form; particular cases are the commutative and anticommutative laws for classical linear algebras. The main result of the paper comprises the freeness theorem mentioned above for subalgebras of a free multioperator algebra, as well as parallel theorems in Shirshov's papers [2] on the freeness of subalgebras of a free commutative and a free anticommutative algebra; the methods of this last article are maintained without essential modifications. 
@article{RM_1969_24_1_a1,
     author = {S. V. Polin},
     title = {Subalgebras of free algebras of some varieties of multioperator algebras},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {15--24},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1969_24_1_a1/}
}
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S. V. Polin. Subalgebras of free algebras of some varieties of multioperator algebras. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 24 (1969) no. 1, pp. 15-24. http://geodesic.mathdoc.fr/item/RM_1969_24_1_a1/