Algorithmic and Combinatorial Algebra (Mathematics and Its Applications #255) (Hardcover)

By L. a. Bokut', G. P. Kukin

Springer, 9780792323136, 384pp.

Publication Date: May 31, 1994

Other Editions of This Title:
Paperback (10/21/2012)

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Description

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).