Grobner Shirshov Bases Normal Forms Combinatorial And Decision Problems In Algebra
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Grobner Shirshov Bases Normal Forms Combinatorial And Decision Problems In Algebra
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Author : Leonid Bokut
language : en
Publisher: World Scientific
Release Date : 2020-06-16
Grobner Shirshov Bases Normal Forms Combinatorial And Decision Problems In Algebra written by Leonid Bokut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-16 with Mathematics categories.
The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac-Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple Lie algebra theory, the plactic monoid theory. One of the main problems for such presentations is the problem of normal forms of their elements. Classical examples of such normal forms give the Poincaré-Birkhoff-Witt theorem for universal enveloping algebras and Artin-Markov normal form theorem for braid groups in Burau generators.What is now called Gröbner-Shirshov bases theory is a general approach to the problem. It was created by a Russian mathematician A I Shirshov (1921-1981) for Lie algebras (explicitly) and associative algebras (implicitly) in 1962. A few years later, H Hironaka created a theory of standard bases for topological commutative algebra and B Buchberger initiated this kind of theory for commutative algebras, the Gröbner basis theory. The Shirshov paper was largely unknown outside Russia. The book covers this gap in the modern mathematical literature. Now Gröbner-Shirshov bases method has many applications both for classical algebraic structures (associative, Lie algebra, groups, semigroups) and new structures (dialgebra, pre-Lie algebra, Rota-Baxter algebra, operads). This is a general and powerful method in algebra.
Gr Bner Shirshov Bases
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Author : Leonid Arkadʹevich Bokutʹ
language : en
Publisher:
Release Date : 2015
Gr Bner Shirshov Bases written by Leonid Arkadʹevich Bokutʹ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Algebra categories.
Advances In Algebra
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Author : K. P. Shum
language : en
Publisher: World Scientific
Release Date : 2003
Advances In Algebra written by K. P. Shum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This is the proceedings of the ICM2002 Satellite Conference on Algebras. Over 175 participants attended the meeting. The opening ceremony included an address by R. Gonchidorsh, former vice-president of the Mongolian Republic in Uaalannbaatar. The topics covered at the conference included general algebras, semigroups, groups, rings, hopf algebras, modules, codes, languages, automation theory, graphs, fuzz algebras and applications.
Combinatorial Problems And Exercises
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Author : László Lovász
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Combinatorial Problems And Exercises written by László Lovász and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems (apart from some general comments at the beginning of each chapter). In the second part, a hint is given for each exercise, which contains the main idea necessary for the solution, but allows the reader to practice theechniques by completing the proof. In the third part, a full solution is provided for each problem. This book will be useful to those students who intend to start research in graph theory, combinatorics or their applications, and for those researchers who feel that combinatorial techniques mightelp them with their work in other branches of mathematics, computer science, management science, electrical engineering and so on. For background, only the elements of linear algebra, group theory, probability and calculus are needed.
Algebraic Operads
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Author : Murray R. Bremner
language : en
Publisher: Chapman & Hall/CRC
Release Date : 2016
Algebraic Operads written by Murray R. Bremner and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Algebra categories.
This book presents a systematic treatment of Gröbner bases in several contexts. The book builds up to the theory of Gröbner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. Throughout the book, both the mathematical theory and computational methods are emphasized and numerous algorithms, examples, and exercises are provided to clarify and illustrate the concrete meaning of abstract theory.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2001
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Algebraic Structures And Applications
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Author : Sergei Silvestrov
language : en
Publisher: Springer Nature
Release Date : 2020-06-18
Algebraic Structures And Applications written by Sergei Silvestrov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-18 with Mathematics categories.
This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas.
Differential Equations From The Algebraic Standpoint
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Author : Joseph Fels Ritt
language : en
Publisher: American Mathematical Soc.
Release Date : 1932-12-31
Differential Equations From The Algebraic Standpoint written by Joseph Fels Ritt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1932-12-31 with Mathematics categories.
This book can be viewed as a first attempt to systematically develop an algebraic theory of nonlinear differential equations, both ordinary and partial. The main goal of the author was to construct a theory of elimination, which ``will reduce the existence problem for a finite or infinite system of algebraic differential equations to the application of the implicit function theorem taken with Cauchy's theorem in the ordinary case and Riquier's in the partial.'' In his 1934 review of the book, J. M. Thomas called it ``concise, readable, original, precise, and stimulating'', and his words still remain true. A more fundamental and complete account of further developments of the algebraic approach to differential equations is given in Ritt's treatise Differential Algebra, written almost 20 years after the present work (Colloquium Publications, Vol. 33, American Mathematical Society, 1950).
Term Rewriting And All That
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Author : Franz Baader
language : en
Publisher: Cambridge University Press
Release Date : 1998
Term Rewriting And All That written by Franz Baader and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Computers categories.
Unified and self-contained introduction to term-rewriting; suited for students or professionals.
Galois Theory Of Linear Differential Equations
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Author : Marius van der Put
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-21
Galois Theory Of Linear Differential Equations written by Marius van der Put and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-21 with Mathematics categories.
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews