Algorithmic and Combinatorial Algebra

the long version

This major volume presents an authoritative overview of developments in algorithmic and combinatorial algebra which have been achieved during the last forty years or so, 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 subalgebras 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 analysing the word and conjugacy problems in the Novikov--Boone groups (Chapters 8 and 9). Many results described here appear for the first time in a monograph. The volume concludes with a discussion of three applications. For graduate students and researchers whose work involves algorithmic and combinatorial algebra and its applications.