Buch, Englisch, 480 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 924 g
Geneses and Applications
Buch, Englisch, 480 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 924 g
ISBN: 978-0-19-853398-6
Verlag: OUP Oxford
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.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Algebra Homologische Algebra
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
Weitere Infos & Material
- 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
