Abstract
In this chapter, we consider the main properties of free algebras of Schreier varieties of algebras. A variety of algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free in the same variety of algebras. In Section 11.1, we describe the main types of Schreier varieties and introduce universal multiplicative enveloping algebras of free algebras. Theorem 11.1.1 gives the main properties of the free algebras of these varieties. In Section 11.2, we expose the weak algorithm for free associative algebras and discuss Schreier’s techniques for free algebras: ranks of left ideals of free associative algebras and Schreier-type formulas for ranks of subalgebras of free algebras.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Mikhalev, A.A., Shpilrain, V., Yu, JT. (2004). Schreier Varieties of Algebras. In: Combinatorial Methods. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21724-6_12
Download citation
DOI: https://doi.org/10.1007/978-0-387-21724-6_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2344-8
Online ISBN: 978-0-387-21724-6
eBook Packages: Springer Book Archive