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Primitive and almost primitive elements of Schreier varieties. (English. Russian original) Zbl 07058838
J. Math. Sci., New York 237, No. 2, 157-179 (2019); translation from Fundam. Prikl. Mat. 21, No. 2, 3-35 (2016).
Summary: 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.
MSC:
08 General algebraic systems
16 Associative rings and algebras
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