Overview

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' nearrings are examined. Some nearrings of maps on a group are reviewed and linked with group-theoretical and geometrical questions. Audience: Researchers working in nearring theory, group theory, semigroup theory, designs, and translation planes. Some of the material will be accessible to graduate students.

Full Product Details

Author:   G. Ferrero
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 2002
Volume:   4
Dimensions:   Width: 16.00cm , Height: 3.30cm , Length: 24.00cm
Weight:   1.002kg
ISBN:  

9781461379690

ISBN 10:   1461379695
Pages:   611
Publication Date:   17 September 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

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 Herstein’s 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 Grönewald and Olivier.- 5.6 A generalization of primary Nöther 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.- 8.2Homogeneous functions.- 8.3 On centralizers of a group of automorphisms.- 8.4 Covers and fibrations.- 8.5 Geometric remarks.

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