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Fundam. Prikl. Mat., 2016, Volume 21, Issue 2, Pages 3–35 (Mi fpm1718)  

Primitive and almost primitive elements of Schreier varieties

V. A. Artamonov, A. V. Klimakov, A. A. Mikhalev, A. V. Mikhalev

Lomonosov Moscow State University

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.

Funding Agency Grant Number
Russian Science Foundation 16-11-10013


Full text: PDF file (306 kB)
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Document Type: Article
UDC: 512.554+512.554.33+512.554.34+512.554.37+512.554.38+512.572,512.573+510.53+512.543+512.544.42+512.544.43

Citation: V. A. Artamonov, A. V. Klimakov, A. A. Mikhalev, A. V. Mikhalev, “Primitive and almost primitive elements of Schreier varieties”, Fundam. Prikl. Mat., 21:2 (2016), 3–35

Citation in format AMSBIB
\Bibitem{ArtKliMik16}
\by V.~A.~Artamonov, A.~V.~Klimakov, A.~A.~Mikhalev, A.~V.~Mikhalev
\paper Primitive and almost primitive elements of Schreier varieties
\jour Fundam. Prikl. Mat.
\yr 2016
\vol 21
\issue 2
\pages 3--35
\mathnet{http://mi.mathnet.ru/fpm1718}
\elib{http://elibrary.ru/item.asp?id=32057805}


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  • Фундаментальная и прикладная математика
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