Bokut L., Chen Y., Kalorkoti K., Kolesnikov P., Lopatkin V.E. Gröbner-Shirshov Bases: Normal Forms, Combinatorial And Decision Problems In Algebra

World Scientific, 2020. — 308 p.Preface
Introduction
The Euclidean algorithm
The Gaussian elimination algorithm
Systems of polynomial equations
Free algebras
Semigroups and groups
Noncommutative polynomials
Free commutative algebras
Free Lie algebras
Composition-Diamond Lemma
Grobner bases for commutative algebras
Grobner–Shirshov bases for associative algebras
Grobner–Shirshov bases for tensor product of free algebras
Grobner–Shirshov bases for Lie algebras
Applications of Grobner–Shirshov bases
Normal form for semigroups and groups
Free product of algebras and groups
Modules over associative algebras
Replicated algebras
Associative conformal algebras
Lifting of Grobner bases to Grobner–Shirshov bases
Lie algebra with unsolvable word problem
Grobner–Shirshov basis for the Drinfeld–Kohno Lie algebra
Grobner-Shirshov bases for Lie algebras over a commutative algebra
Preliminaries
Composition-Diamond lemma for Liek[Y ](X)
Examples of Shirshov and Cartier
Cohn conjecture
Other applications
Decision problems for groups
Decision problems
Computability
Group theoretic tools
Unsolvability of the word and conjugacy problems for finitely presented groups
The word problem and r.e. Turing degrees
The Higman embedding theorem
The conjugacy problem and r.e. Turing degrees
(Co)Homology and Gr¨obner–Shirshov basis
Preliminaries
Algebraic discrete Morse theory
Group extensions
(Singular) Extensions of Algebras
Bibliography
Index