Abstract
In the work of A.G. Kurosh [2] it is proved that every subalgebra of a free nonassociative algebra is free. It would be natural to investigate the possibility of transferring this theorem to the most important classes of relatively free algebras whose general definition was given in the work of A.I. Malcev [3].
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References
M. Hall, A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950) 575–581.
A.G. Kurosh, Nonassociative free algebras and free products of algebras, Mat. Sbornik N.S. 20 (1947) 239–262.
A.I. Malcev, On algebras defined by identical relations, Mat. Sbornik N.S. 26 (1950) 19–33.
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© 2009 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland
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Shirshov, A.I. (2009). Subalgebras of Free Lie Algebras. In: Bokut, L., Shestakov, I., Latyshev, V., Zelmanov, E. (eds) Selected Works of A.I. Shirshov. Contemporary Mathematicians. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8858-4_1
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DOI: https://doi.org/10.1007/978-3-7643-8858-4_1
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