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 : 4.09/5 ( download)

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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.

Author : Leonid Arkadʹevich Bokutʹ
Publisher :
ISBN 13 : 9789814619493
Total Pages : 308 pages
Book Rating : 4.93/5 ( download)

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Download or read book Gröbner-Shirshov Bases written by Leonid Arkadʹevich Bokutʹ and published by . This book was released on 2015 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Gilbert Baumslag
Publisher : Springer Science & Business Media
ISBN 13 : 1461397308
Total Pages : 235 pages
Book Rating : 4.04/5 ( download)

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Download or read book Algorithms and Classification in Combinatorial Group Theory written by Gilbert Baumslag and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.

Author : A.I. Kostrikin
Publisher : Springer
ISBN 13 : 9783642081248
Total Pages : 290 pages
Book Rating : 4.4X/5 ( download)

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Download or read book Algebra VI written by A.I. Kostrikin and published by Springer. This book was released on 2011-12-12 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains two self-contained surveys of key aspects of algebra, complete with definitions and simple properties and references to proofs in the literature. The book will be of great interest to graduate students and researchers in mathematics, computer science and theoretical physics.

Author : Kenji Iohara
Publisher : Springer Nature
ISBN 13 : 3030264548
Total Pages : 375 pages
Book Rating : 4.43/5 ( download)

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Download or read book Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers written by Kenji Iohara and published by Springer Nature. This book was released on 2020-02-20 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.

Author : K. P. Shum
Publisher :
ISBN 13 : 9811215472
Total Pages : 498 pages
Book Rating : 4.76/5 ( download)

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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:

Author : Fengming Dong
Publisher : World Scientific
ISBN 13 : 9814480460
Total Pages : 386 pages
Book Rating : 4.68/5 ( download)

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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.

Author : László Fuchs
Publisher : American Mathematical Soc.
ISBN 13 : 0821819631
Total Pages : 633 pages
Book Rating : 4.30/5 ( download)

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Download or read book Modules over Non-Noetherian Domains written by László Fuchs and published by American Mathematical Soc.. This book was released on 2001 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors present both traditional and modern discoveries in the subject area, concentrating on advanced aspects of the topic. Existing material is studied in detail, including finitely generated modules, projective and injective modules, and the theory of torsion and torsion-free modules. Some topics are treated from a new point of view. Also included are areas not found in current texts, for example, pure-injectivity, divisible modules, uniserial modules, etc. Special emphasis is given to results that are valid over arbitrary domains. The authors concentrate on modules over valuation and Prüfer domains, but also discuss Krull and Matlis domains, h-local, reflexive, and coherent domains. The volume can serve as a standard reference book for specialists working in the area and also is a suitable text for advanced-graduate algebra courses and seminars.

Author : Lisa Iannucci
Publisher : Penguin
ISBN 13 : 1101140623
Total Pages : 393 pages
Book Rating : 4.28/5 ( download)

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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

Author : Hibi Takayuki
Publisher : World Scientific
ISBN 13 : 9811200491
Total Pages : 476 pages
Book Rating : 4.96/5 ( download)

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Download or read book Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes written by Hibi Takayuki and published by World Scientific. This book was released on 2019-05-30 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.