Nearrings

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.