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Subalgebras of Free Commutative and Free Anticommutative Algebras

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Selected Works of A.I. Shirshov

Part of the book series: Contemporary Mathematicians ((CM))

Abstract

1. It is known [2] that any subalgebra of the free nonassociative algebra is free. It is natural to ask the corresponding question for relatively free algebras [3], of course restricting oneself to the most important classes of algebras.

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References

  1. M. Hall, A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950) 575–581.

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  2. A.G. Kurosh, Nonassociative free algebras and free products of algebras, Mat. Sbornik N.S. 20 (1947) 239–262.

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  3. A.I. Malcev, On algebras defined by identical relations, Mat. Sbornik N.S. 26 (1950) 19–33.

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  4. A.I. Shirshov, Subalgebras of free Lie algebras, Mat. Sbornik N.S. 33 (1953) 441–45.

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Authors
  1. A. I. Shirshov
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Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Koptyuga, 4, 630090, Novosibirsk, Russia

    Leonid Bokut

  2. IME-USP Ruodo Matao, 1010 Cidade Universitaria, CEP 05508-090, Sao Paulo, SP, Brasil

    Ivan Shestakov

  3. Mehmat MGU im. Lomonosova, Vorob’evy Gory, 119899, Moscow, Russia

    Victor Latyshev

  4. Dep. of Mathematics, UCSD, 9500 Gilman Drive #0112, La Jolla, CA, 92093-0112, USA

    Efim Zelmanov

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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 Commutative and Free Anticommutative 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_3

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