Nearrings: Geneses and Applications
Geneses and Applications
Published on 19. November 1992
Book
Hardback
480 pages
978-0-19-853398-6 (ISBN)
Description
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.
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.
Reviews / Votes
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 *More details
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Illustrations
2 Zeichnungen
2 line drawings
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 33 mm
Weight
924 gr
ISBN-13
978-0-19-853398-6 (9780198533986)
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Schweitzer Classification
Person
Content
CHAPTER 1: INTRODUCTION TO NEARRINGS ; CHAPTER 2: PLANAR NEARRINGS ; CHAPTER 3: THE GREAT UNIFIER ; CHAPTER 4: SOME FIRST FAMILIES OF NEARRINGS AND SOME OF THEIR IDEALS ; CHAPTER 5: SOME STRUCTURE OF GROUPS OF UNITS ; CHAPTER 6: AVANT-GARDE FAMILIES OF NEARRINGS