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Rings, Fields and Groups

Rings, Fields and Groups PDF Author: R. B. J. T. Allenby
Publisher: Butterworth-Heinemann
ISBN: 9780340544402
Category : Mathematics
Languages : en
Pages : 383

Book Description
Provides an introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses

Rings, Fields and Groups

Rings, Fields and Groups PDF Author: R. B. J. T. Allenby
Publisher: Butterworth-Heinemann
ISBN: 9780340544402
Category : Mathematics
Languages : en
Pages : 383

Book Description
Provides an introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses

Fields and Rings

Fields and Rings PDF Author: Irving Kaplansky
Publisher: University of Chicago Press
ISBN: 0226424510
Category : Mathematics
Languages : en
Pages : 217

Book Description
This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews

Rings, Fields, and Vector Spaces

Rings, Fields, and Vector Spaces PDF Author: Bharath Sethuraman
Publisher: Springer Science & Business Media
ISBN: 0387948481
Category : Mathematics
Languages : en
Pages : 210

Book Description
Using the proof of the non-trisectability of an arbitrary angle as a final goal, the author develops in an easy conversational style the basics of rings, fields, and vector spaces. Originally developed as a text for an introduction to algebra course for future high-school teachers at California State University, Northridge, the focus of this book is on exposition. It would serve extremely well as a focused, one-semester introduction to abstract algebra.

Applied Discrete Structures

Applied Discrete Structures PDF Author: Ken Levasseur
Publisher: Lulu.com
ISBN: 1105559297
Category : Applied mathematics
Languages : en
Pages : 574

Book Description
Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.

Groups, Rings and Fields

Groups, Rings and Fields PDF Author: David A.R. Wallace
Publisher: Springer Science & Business Media
ISBN: 1447104250
Category : Mathematics
Languages : en
Pages : 256

Book Description
This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.

A Guide to Groups, Rings, and Fields

A Guide to Groups, Rings, and Fields PDF Author: Fernando Q. Gouvêa
Publisher: American Mathematical Soc.
ISBN: 1614442118
Category : Mathematics
Languages : en
Pages : 309

Book Description
Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.

Galois Fields and Galois Rings Made Easy

Galois Fields and Galois Rings Made Easy PDF Author: Maurice Kibler
Publisher: Elsevier
ISBN: 0081023510
Category : Mathematics
Languages : en
Pages : 272

Book Description
This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics. The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access. This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering). Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics. Contains numerous examples that accompany the text Includes an important chapter on mutually unbiased bases Helps physicists and theoretical chemists understand this area of mathematics

Lectures on Finite Fields and Galois Rings

Lectures on Finite Fields and Galois Rings PDF Author: Zhe-Xian Wan
Publisher: World Scientific
ISBN: 9789812385703
Category : Mathematics
Languages : en
Pages : 360

Book Description
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.

A First Course in Abstract Algebra

A First Course in Abstract Algebra PDF Author: Marlow Anderson
Publisher: CRC Press
ISBN: 1420057111
Category : Mathematics
Languages : en
Pages : 684

Book Description
Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there

Algebra

Algebra PDF Author: Louis Rowen
Publisher: CRC Press
ISBN: 1439863520
Category : Mathematics
Languages : en
Pages : 264

Book Description
This text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material. From the table of contents: - Groups: Monoids and Groups - Cauchyís Theorem - Normal Subgroups - Classifying Groups - Finite Abelian Groups - Generators and Relations - When Is a Group a Group? (Cayley's Theorem) - Sylow Subgroups - Solvable Groups - Rings and Polynomials: An Introduction to Rings - The Structure Theory of Rings - The Field of Fractions - Polynomials and Euclidean Domains - Principal Ideal Domains - Famous Results from Number Theory - I Fields: Field Extensions - Finite Fields - The Galois Correspondence - Applications of the Galois Correspondence - Solving Equations by Radicals - Transcendental Numbers: e and p - Skew Field Theory - Each chapter includes a set of exercises