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Combinatorial Methods Free Groups, Polynomials, and Free Algebras

Title
Combinatorial Methods [electronic resource] : Free Groups, Polynomials, and Free Algebras / by Alexander A. Mikhalev, Vladimir Shpilrain, Jie-Tai Yu.
ISBN
9780387217246
Published
New York, NY : Springer New York : Imprint: Springer, 2004.
Physical Description
1 online resource.
Local Notes
Access is available to the Yale community.
Access and use
Access restricted by licensing agreement.
Summary
<P>�The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.</P> <P>This book is divided into three fairly independent parts. Part I provides a brief exposition of several classical techniques in combinatorial group theory, namely, methods of Nielsen, Whitehead, and Tietze. Part II contains the main focus of the book. Here the authors show how the aforementioned techniques of combinatorial group theory found their way into affine algebraic geometry, a fascinating area of mathematics that studies polynomials and polynomial mappings. Part III illustrates how ideas from combinatorial group theory contributed to the theory of free algebras. The focus here is on 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).</P>
Variant and related titles
Springer ebooks.
Other formats
Printed edition:
Format
Books / Online
Language
English
Added to Catalog
January 28, 2013
Series
CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
Contents
<P>Preface
Introduction
<STRONG>I. Groups</STRONG>: Introduction. Classical Techniques. Test Elements. Other Special Elements. Automorphic Orbits
<STRONG>II. Polynomial Algebras</STRONG>: Introduction. The Jacobian Conjecture. The Cancellation Conjecture. Nagata's Problem. The Embedding Problem. Coordinate Polynomials. Test Polynomials
<STRONG>III. Free Nielsen-Schreier Algebras</STRONG>: Introduction. Schreier Varieties of Algebras. Rank Theorems and Primitive Elements. Generalized Primitive Elements. Free Leibniz Algebras
References
Notations
Author Index
Subject Index.</P>.
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