Nearrings : geneses and applications
著者
書誌事項
Nearrings : geneses and applications
（Oxford science publications）
Tokyo : Oxford University Press, 1992
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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
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