Abstract Algebra: Introduction to Groups, Rings and Fields With Applications: Introduction to Groups, Rings and Fields with Applications (Second Edition) - Rilegato

Reis, Clive; Rankin, Stuart A.

Rilegato

ISBN 10: 981473053X ISBN 13: 9789814730532

Casa editrice: World Scientific Pub Co Inc, 2016

Riassunto

This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: PolyaBurnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced via congruence classes to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.

Dettagli dell'edizione

• Editore: World Scientific Pub Co Inc
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 981473053X
• ISBN 13: 9789814730532
• Rilegatura: Copertina rigida
• Numero edizione: 2
• Numero di pagine: 555
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile