Algorithmic and Combinatorial Algebra: 255 (Mathematics and Its Applications, 255) - Hardcover

Bokut', L.A.; Kukin, G.P..

Hardcover

ISBN 10: 0792323130 ISBN 13: 9780792323136

Publisher: Springer, 1994

Synopsis

Even three decades ago, the words 'combinatorial algebra' contrasting, for in­ stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap­ pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef­ fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above).

About this title

Product Description

Algorithmic and Combinatorial Algebra This volume presents an authoritative overview of developments in algorithmic and combinatorial algebra which have been achieved during the past 40 years, with an emphasis on the results obtained by the Novosibirsk school of A.I. Mal'tchev and A.I. Shirshov and followers.

Synopsis

This volume presents an authoritative overview of developments in algorithmic and combinatorial algebra which have been achieved during the past 40 years, with an emphasis on the results obtained by the Novosibirsk school of A.I. Mal'tchev and A.I. Shirshov and followers. The book has nine chapters. These deal with Applications of the Composition (or Diamond) Lemma to associative and Lie algebras (Chapters 1 and 3), to sub-algebras of free Lie algebras and free products of Lie algebras (Chapters 2 and 4), to word problems and embedding theorems in varieties of Lie algebras and groups (Chapters 5-7) and to the constructive theory of HNN-extensions and its use in analyzing the word and conjugacy problems in the Novikov Boone groups (Chapters 8 and 9). The volume concludes with a discussion of three applications. It is designed for graduate students and researchers whose work involves algorithmic and combinatorial algebra and its applications.

Edition details

• Publisher: Springer
• Publication date: 1994
• Language: English
• ISBN 10: 0792323130
• ISBN 13: 9780792323136
• Binding: Hardcover
• Number of pages: 400