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.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.