Algorithmic and Combinatorial Algebra

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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.