Email this article Primitive and Almost Primitive Elements of Schreier Varieties
- Authors: Artamonov V.A.1, Klimakov A.V.1, Mikhalev A.A.1, Mikhalev A.V.1
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Affiliations:
- Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University
- Issue: Vol 237, No 2 (2019)
- Pages: 157-179
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242312
- DOI: https://doi.org/10.1007/s10958-019-4148-2
- ID: 242312
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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.
About the authors
V. A. Artamonov
Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University
Email: aamikhalev@mail.ru
Russian Federation, Moscow
A. V. Klimakov
Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University
Email: aamikhalev@mail.ru
Russian Federation, Moscow
A. A. Mikhalev
Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University
Author for correspondence.
Email: aamikhalev@mail.ru
Russian Federation, Moscow
A. V. Mikhalev
Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University
Email: aamikhalev@mail.ru
Russian Federation, Moscow
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