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

Author : Leonid Bokut
Publisher : World Scientific
ISBN 13 : 9814619507
Total Pages : 308 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Grobner-shirshov Bases: Normal Forms, Combinatorial And Decision Problems In Algebra by : Leonid Bokut

Download or read book Grobner-shirshov Bases: Normal Forms, Combinatorial And Decision Problems In Algebra written by Leonid Bokut and published by World Scientific. This book was released on 2020-06-16 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Grobner-Shirshov Bases: Normal Forms, Combinatorial and Decision Problems in Algebra

Author : Leonid Bokut
Publisher : World Scientific Publishing Company
ISBN 13 : 9789814619486
Total Pages : 450 pages
Book Rating : 4.6/5 (194 download)

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Book Synopsis Grobner-Shirshov Bases: Normal Forms, Combinatorial and Decision Problems in Algebra by : Leonid Bokut

Download or read book Grobner-Shirshov Bases: Normal Forms, Combinatorial and Decision Problems in Algebra written by Leonid Bokut and published by World Scientific Publishing Company. This book was released on 2018 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances in Algebra

Author : K. P. Shum
Publisher : World Scientific
ISBN 13 : 9812705805
Total Pages : 531 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Advances in Algebra by : K. P. Shum

Download or read book Advances in Algebra written by K. P. Shum and published by World Scientific. This book was released on 2003 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Operads

Author : Murray R. Bremner
Publisher : CRC Press
ISBN 13 : 1482248573
Total Pages : 382 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Algebraic Operads by : Murray R. Bremner

Download or read book Algebraic Operads written by Murray R. Bremner and published by CRC Press. This book was released on 2016-04-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of Grobner bases in several contexts. The book builds up to the theory of Grobner 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.

Combinatorial Problems and Exercises

Author : L. Lovász
Publisher : Elsevier
ISBN 13 : 0080933092
Total Pages : 636 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Combinatorial Problems and Exercises by : L. Lovász

Download or read book Combinatorial Problems and Exercises written by L. Lovász and published by Elsevier. This book was released on 2014-06-28 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book.Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 888 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Foundations of Garside Theory

Author : Patrick Dehornoy
Publisher : Erich Schmidt Verlag GmbH & Co. KG
ISBN 13 : 9783037191392
Total Pages : 714 pages
Book Rating : 4.1/5 (913 download)

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Book Synopsis Foundations of Garside Theory by : Patrick Dehornoy

Download or read book Foundations of Garside Theory written by Patrick Dehornoy and published by Erich Schmidt Verlag GmbH & Co. KG. This book was released on 2015 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a monograph on algebra, with connections to geometry and low-dimensional topology. It mainly involves groups, monoids, and categories, and aims to provide a unified treatment for those situations in which one can find distinguished decompositions by iteratively extracting a maximal fragment lying in a prescribed family. Initiated in 1969 by F. A. Garside in the case of Artin's braid groups, this approach led to interesting results in a number of cases, the central notion being what the authors call a Garside family. The study is far from complete, and the purpose of this book is to present the current state of the theory and to invite further research. The book has two parts: In Part A, the bases of a general theory, including many easy examples, are developed. In Part B, various more sophisticated examples are specifically addressed. To make the content accessible to a wide audience of nonspecialists, the book's exposition is essentially self-contained and very few prerequisites are needed. In particular, it should be easy to use this as a textbook both for Garside theory and for the more specialized topics investigated in Part B: Artin-Tits groups, Deligne-Lusztig varieties, groups of algebraic laws, ordered groups, and structure groups of set-theoretic solutions of the Yang-Baxter equation. The first part of the book can be used as the basis for a graduate or advanced undergraduate course.

New Trends in Algebras and Combinatorics

Author : K. P. Shum
Publisher :
ISBN 13 : 9811215472
Total Pages : 498 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis New Trends in Algebras and Combinatorics by : K. P. Shum

Download or read book New Trends in Algebras and Combinatorics written by K. P. Shum and published by . This book was released on 2020 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebra.

Author : Kostrikin, Aleksei Ivanovich Kostrikin
Publisher :
ISBN 13 : 9780387546995
Total Pages : 287 pages
Book Rating : 4.5/5 (469 download)

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Book Synopsis Algebra. by : Kostrikin, Aleksei Ivanovich Kostrikin

Download or read book Algebra. written by Kostrikin, Aleksei Ivanovich Kostrikin and published by . This book was released on 1990 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Structures and Applications

Author : Sergei Silvestrov
Publisher : Springer Nature
ISBN 13 : 3030418502
Total Pages : 976 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Algebraic Structures and Applications by : Sergei Silvestrov

Download or read book Algebraic Structures and Applications written by Sergei Silvestrov and published by Springer Nature. This book was released on 2020-06-18 with total page 976 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fields of Logic and Computation III

Author : Andreas Blass
Publisher : Springer Nature
ISBN 13 : 3030480062
Total Pages : 349 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Fields of Logic and Computation III by : Andreas Blass

Download or read book Fields of Logic and Computation III written by Andreas Blass and published by Springer Nature. This book was released on 2020-05-22 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift is published in honor of Yuri Gurevich’s 80th birthday. An associated conference, YuriFest 2020, was planned for May 18–20 in Fontainebleau, France, in combination with the 39th Journées sur les Arithmétiques Faibles also celebrating Yuri’s 80th birthday. Because of the coronavirus situation, the conference had to be postponed, but this Festschrift is being published as originally planned. It addresses a very wide variety of topics, but by no means all of the fields of logic and computation in which Yuri has made important progress.

Ring and Module Theory

Author : Toma Albu
Publisher : Springer Science & Business Media
ISBN 13 : 3034600070
Total Pages : 204 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Ring and Module Theory by : Toma Albu

Download or read book Ring and Module Theory written by Toma Albu and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.

Combinatorial and Geometric Group Theory

Author : Oleg Bogopolski
Publisher : Springer Science & Business Media
ISBN 13 : 3764399112
Total Pages : 318 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Combinatorial and Geometric Group Theory by : Oleg Bogopolski

Download or read book Combinatorial and Geometric Group Theory written by Oleg Bogopolski and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.

Differential Equations from the Algebraic Standpoint

Author : Joseph Fels Ritt
Publisher : American Mathematical Soc.
ISBN 13 : 0821846051
Total Pages : 184 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Differential Equations from the Algebraic Standpoint by : Joseph Fels Ritt

Download or read book Differential Equations from the Algebraic Standpoint written by Joseph Fels Ritt and published by American Mathematical Soc.. This book was released on 1932-12-31 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Gradings on Simple Lie Algebras

Author : Alberto Elduque
Publisher : American Mathematical Soc.
ISBN 13 : 0821898469
Total Pages : 355 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Gradings on Simple Lie Algebras by : Alberto Elduque

Download or read book Gradings on Simple Lie Algebras written by Alberto Elduque and published by American Mathematical Soc.. This book was released on 2013 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some non-classical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form.

The Complete Idiot's Guide to Success as a Property Manager

Author : Lisa Iannucci
Publisher : Penguin
ISBN 13 : 1101140623
Total Pages : 393 pages
Book Rating : 4.1/5 (11 download)

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Book Synopsis The Complete Idiot's Guide to Success as a Property Manager by : Lisa Iannucci

Download or read book The Complete Idiot's Guide to Success as a Property Manager written by Lisa Iannucci and published by Penguin. This book was released on 2009-10-06 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Invaluable advice for property managers-and how to keep an eye on the prize Property managers often lose sight of advancing their careers because they get buried in the details of labor-intensive, day–to–day management. This guide helps the harried professional keep priorities straight with: advice on education, certifications and licenses; an overview of property management skills; information about regulations, finances, taxes, safety codes; advice on time management, prioritizing duties, and supervising staff; and how to start a property management business. • Author is an experience certified Property Manager • Easy, accessible, jargon-free style • Concrete advice about everything from emergencies to boiler maintenance to building finances

Chromatic Polynomials And Chromaticity Of Graphs

Author : Fengming Dong
Publisher : World Scientific
ISBN 13 : 9814480460
Total Pages : 386 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Chromatic Polynomials And Chromaticity Of Graphs by : Fengming Dong

Download or read book Chromatic Polynomials And Chromaticity Of Graphs written by Fengming Dong and published by World Scientific. This book was released on 2005-06-23 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book into three main parts, the authors take readers from the rudiments of chromatic polynomials to more complex topics: the chromatic equivalence classes of graphs and the zeros and inequalities of chromatic polynomials. The early material is well suited to a graduate level course while the latter parts will be an invaluable resource for postgraduate students and researchers in combinatorics and graph theory.