Overview

Nearrings arise naturally in various ways, but most nearrings studied today arise as the endomorphisms of a group or cogroup object of a category. These nearrings are rings if the group object is also a cogroup object. During the first half of the twentieth century, nearfields were formalized and applications to sharply transitive groups and to foundations of geometry were utilized. Planar nearrings grew out of the geometric success of the planar nearfields and have found numerous applications to various branches of mathematics as well as to coding theory, cryptography, the design of statistical experiments, families of mutually orthogonal Latin squares and constructing planes with circles having radius and centre even though there is no metric involved. Even though nearrings may lack the extra symmetry of a ring, there is often a very sophisticated elegance in their structure. It has recently been observed that there is an abundance of symmetry in finite cirucular planar nearrings, which disappear if the nearring is a ring.

Full Product Details

Author:   James R. Clay (Professor of Mathematics, Department of Mathematics, Professor of Mathematics, Department of Mathematics, University of Arizona, Tucson)
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Dimensions:   Width: 16.30cm , Height: 3.20cm , Length: 24.20cm
Weight:   0.952kg
ISBN:  

9780198533986

ISBN 10:   0198533985
Pages:   480
Publication Date:   19 November 1992
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.

Table of Contents

Chapter 1: Introduction to nearrings 1.1: Getting acquainted 1.2: Lots of examples 1.3: Many cheerful facts about nearrings Chapter 2: Planar Nearrings 2.1: Planarity for nearrings 2.2: Construction of circular planar nearrings 2.3: Geometry of curcular planar nearrings 2.4: Other geometric structures from planar nearrings 2.5: Coding, cryptography, and combinatorics 2.6: Sharply transitive groups and nondesarguesian planes Chapter 3: The great unifier 3.1: A little category theory 3.2: Group and cogroup objects 3.4: Examples Chapter 4: Some first families of nearrings and some of their ideals 4.1: First. what is a nearring module? 4.2: Centralizer and transformation nearrings 4.3: Distributively generated nearrings 4.4: The ideals of abstract affine nearrings 4.5: Polynomial nearrings 4.6: Power series nearrings Chapter 5: Some structure of groups of units 5.1: Preliminaries 5.2: Direct products in groups of units 5.3: Semidirect products and wreath products 5.4: Group extensions with factor sets 5.5: A mixture of the above Chapter 6: Avant-garde families of nearrings 6.1: Sandwich and laminated nearrings 6.2: Syntactic nearrings 6.3: The cornucopia Appendix: Various diagrams List of symbols Bibliography Index

Reviews

The material presented in this book has been chosen so that the book emphasizes the applications and provides the foundation for their serious study. The book is carefully written and is accessible to those with a good foundation in algebra, and an acquaintance with point set topology, which is needed in a few places. Mathematical Reviews Issue 94b At times, the reader has the feeling of being spoken to by an author, and there is often an informality and lightness of touch in his approach. Another pleasant aspect of this book is an emphasis on examples, particularly those that triggered further developments in the subject, and also on problems of all kinds, especially open-ended questions leading to further research. The book complements well the existing books on the subject, and there is remarkably little overlap ... this book is very useful ... a book worth buying by all libraries and any individual interested in any of the theory or applications covered. J.D.P. Meldrum, Bulletin of the London Mathematical Society, 27 (1995) a very useful addition to the literature on near-rings ... there is the pleasant and light approach of the author which makes the material easier to read, particularly in those parts where the nature of the material makes for heavy going ... This book can be thoroughly recommended. J.D.P. Meldrum, Besprechungsbelege, February 1994

<br> Excellent. The material presented in this book has been chosen so that the book emphasizes the applications and provides the foundation for their serious study. . . . carefully written and is accessible. -- aroslav Libicher, Mathematical Reviews<br>

Excellent. The material presented in this book has been chosen so that the book emphasizes the applications and provides the foundation for their serious study. . . . carefully written and is accessible. -- aroslav Libicher, Mathematical Reviews<br>

Excellent. The material presented in this book has been chosen so that the book emphasizes the applications and provides the foundation for their serious study. . . . carefully written and is accessible. -- aroslav Libicher, Mathematical Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions