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Journal of Mathematical Sciences

, Volume 237, Issue 2, pp 157–179 | Cite as

Primitive and Almost Primitive Elements of Schreier Varieties

  • V. A. Artamonov
  • A. V. Klimakov
  • A. A. MikhalevEmail author
  • A. V. Mikhalev
Article
  • 6 Downloads

Abstract

A variety of linear algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free. A system of elements of a free algebra is primitive if there is a complement of this system with respect to a free generating set of the free algebra. An element of a free algebra of a Schreier variety is said to be almost primitive if it is not primitive in the free algebra, but it is a primitive element of any subalgebra that contains it. This survey article is devoted to the study of primitive and almost primitive elements of Schreier varieties.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • V. A. Artamonov
    • 1
  • A. V. Klimakov
    • 1
  • A. A. Mikhalev
    • 1
    Email author
  • A. V. Mikhalev
    • 1
  1. 1.Faculty of Mechanics and MathematicsM. V. Lomonosov Moscow State UniversityMoscowRussia

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