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Nearrings : some developments linked to semigroups and groups /

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This work presents new and old constructions of nearrings. Links between properties of the multiplicative of nearrings (as regularity conditions and identities) and the structure of nearrings are studied. Primality and minimality properties of ideals are collected. Some types of `simpler' nearr...

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Bibliographic Details
Main Author: Cotti Ferrero, Celestina
Corporate Author: SpringerLink (Online service)
Other Authors: Ferrero, Giovanni
Format: eBook
Language:English
Published: Dordrecht ; Boston : Kluwer Academic Publishers, [2002]
Series:Advances in mathematics (Kluwer Academic Publishers) ; v. 4.
Subjects:
Near-rings.
Fastring.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. Elements
  • 1.1 Notations and terminology
  • 1.2 Definitions and first examples
  • 1.3 Clay functions and elementary properties
  • 1.4 Polynomial nearrings
  • 1.5 Axiomatical and geometric questions
  • 1.6 Ideals
  • 1.7 Distributivity conditions
  • 1.8 Maps
  • 1.9 Modules
  • 1.10 On radicals
  • 1.11 Density and interpolation
  • 1.12 Group and matrix nearrings
  • 1.13 Quasi-local nearrings
  • 1.14 Varieties
  • 2. Constructions
  • 2.1 Global constructions
  • 2.2 Orbits of Clay semigroups
  • 2.3 Syntactic nearrings
  • 2.4 Deforming the product
  • 2.5 Deforming the sum
  • 3. Regularities
  • 3.1 Idempotents in nearrings
  • 3.2 Reduced nearrings
  • 3.3 Regularity conditions
  • 3.4 Regular and right strongly regular nearrings
  • 3.5 Generalized nearfields
  • 3.6 Stable and bipotent nearrings
  • 3.7 Some nearrings are nearfields
  • 4. Multiplicative Identities
  • 4.1 Permutation identities
  • 4.2 Commutativity conditions
  • 4.3 Hersteins condition
  • 4.4 Particular periodic nearrings
  • 4.5 Derivations
  • 5. Prime and Minimal
  • 5.1 Prime and semiprime ideals
  • 5.2 M-systems
  • 5.3 On hereditariness of the i-prime nearrings
  • 5.4 Links among various types of primeness
  • 5.5 Regularities and primenesses according to Grnewald and Olivier
  • 5.6 A generalization of primary Nther decomposition
  • 5.7 Minimal ideals
  • 6. Simpler Nearrings
  • 6.1 Groups hosting only trivial nearrings
  • 6.2 Strictly simple nearrings
  • 6.3 On n-simple and n-strictly simple nearrings
  • 6.4 Weakly divisible nearrings
  • 6.5 H-integral nearrings
  • 7. Maps
  • 7.1 Generalizations of homomorphisms
  • 7.2 Endomorphism nearrings
  • 7.3 Endomorphism nearrings can be rings
  • 7.4 Nearrings of maps with condition on the images
  • 7.5 Coincidence problems
  • 7.6 The isomorphism problem
  • 8. Centralizers
  • 8.1 Introductory remarks
  • 8.2 Homogeneous functions
  • 8.3 On centralizers of a group of automorphisms
  • 8.4 Covers and fibrations
  • 8.5 Geometric remarks.