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Book: Combinatorial Methods: Free groups, Polynomials, and Free Algebras
Title  Combinatorial Methods: Free groups, Polynomials, and Free Algebras 

Authors  
Issue Date  2003 
Publisher  SpringerVerlag. 
Citation  Shpilrain, V, Mikhalev, AA and Yu, J. Combinatorial Methods: Free groups, Polynomials, and Free Algebras. New York: SpringerVerlag, 2003 How to Cite? 
Abstract  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 lowdimensional topology in the beginning of the 20th Century.
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). 
Persistent Identifier  http://hdl.handle.net/10722/119230 
ISBN  
ISSN  
Series/Report no.  CMS Books in Mathematics 
DC Field  Value  Language 

dc.contributor.author  Shpilrain, V  en_HK 
dc.contributor.author  Mikhalev, AA  en_HK 
dc.contributor.author  Yu, J  en_HK 
dc.date.accessioned  20100926T08:41:58Z   
dc.date.available  20100926T08:41:58Z   
dc.date.issued  2003  en_HK 
dc.identifier.citation  Shpilrain, V, Mikhalev, AA and Yu, J. Combinatorial Methods: Free groups, Polynomials, and Free Algebras. New York: SpringerVerlag, 2003   
dc.identifier.isbn  9780387405629   
dc.identifier.issn  16135237   
dc.identifier.uri  http://hdl.handle.net/10722/119230   
dc.description.abstract  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 lowdimensional topology in the beginning of the 20th Century. 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).   
dc.language  eng  en_HK 
dc.publisher  SpringerVerlag.  en_HK 
dc.relation.ispartofseries  CMS Books in Mathematics   
dc.title  Combinatorial Methods: Free groups, Polynomials, and Free Algebras  en_HK 
dc.type  Book  en_HK 
dc.identifier.email  Yu, J: yujt@hkusua.hku.hk  en_HK 
dc.identifier.email  Shpilrain, V: shpil@submaths.hku.hk  en_HK 
dc.identifier.email  Mikhalev, AA: sasha@submaths.hku.hk  en_HK 
dc.identifier.authority  Yu, J=rp00834  en_HK 
dc.identifier.doi  10.1007/9780387217246   
dc.identifier.hkuros  85609  en_HK 
dc.identifier.spage  312  en_HK 