Near-rings: The Theory and its Applications
Elsevier (Publisher)
Published on 10. October 2011
469 pages
978-0-08-087134-9 (ISBN)
Description
Near-rings: The Theory and its Applications
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Content
- Front Cover
- Near-Rings
- Copyright Page
- Contents
- Interdependence Guide
- Preface to the Second Edition
- From the Preface to the First Edition
- § 0 Prerequisites
- Part I: Near-Rings for Beginners
- Chapter § 1 The Elementary Theory of Near-Rings
- a) Fundamental Definitions and Properties
- b) Constructions
- c) Embeddings
- d) Some Axiomatic Considerations
- Chapter § 2 Ideal Theory
- a) Sums
- b) Chain Conditions
- c) Decomposition Theorems
- d) Prime Ideals
- e) Nil and Nilpotent
- PART ll: Structure Theory
- Chapter § 3 Elements of the Structure Theory
- a) Types of N-Groups
- b) Change of the Near-Ring
- c) Modularity
- d) Quasiregularity
- e) Idempotents
- f) More on Minimality
- Chapter § 4 Primitive Near-Rings
- a) General
- b) 0-Primitive Near-Rings
- C) 1-Primitive Near-Rings
- d) 2-Primitive Near-Rings
- Chapter § 5 Radical Theory
- a) Jacobson-Typs Radicals: Common Theory
- b) Jacobson-Type Radicals: Special Theory
- c ) The Nil Radical
- d) The Prime Radical
- e) Concluding Remarks
- Part III: Special Classes of Near-Rings
- Chapter § 6 Distributively Generated Near-Rings
- a ) Elementary
- b) Some Axiomatics
- C) Constructions of D.G. Near-Rings
- D) Distributively Generated Near-Rings with Finiteness Conditions
- E) "Free" Distributively Generated Near-Rings
- f ) D-Groups and (N,D)-Groups
- g) Structure Theory
- Chapter § 7 Transformation Near-Rings
- a) MOH(G)
- b) MOH(G)
- c) E(G), A(G) AND I(G)
- d) Polynomial Near-Rings
- Chapter § 8 Near-Fields and Planar Near-Rings
- a) Near-Fields
- b) Planar Near-Rings
- Chapter § 9 More Classes of Near-Rings
- a) IFP - Near-Rings
- b) Near-Rings Without
- C) Affine Near- Rings
- d Near-Rings on given Groups
- e) Ordered Near-Rings
- f ) Regular Near-Rings
- g) Tame Near-Rings
- h) Bicentralizer Near-Rings
- i) Near-Rings and Automata
- j) Miscellaneous Topics
- Appendix
- Near-Rings of Low Order
- 222 Remarkable Examples and Counterexamples
- List of Open Problems
- Bibliography
- Supplementar Works
- List of Symbols and Abbreviations
- Index
