Author | Ferrero, Celestina Cotti. author |
---|---|
Title | Nearrings [electronic resource] : Some Developments Linked to Semigroups and Groups / by Celestina Cotti Ferrero, Giovanni Ferrero |
Imprint | Boston, MA : Springer US, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-0267-4 |
Descript | XX, 611 p. online resource |
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 Hersteinโs 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 Grรถnewald and Olivier -- 5.6 A generalization of primary Nรถther decomposition -- 5.7 Minimal ideals -- 6. โSimplerโ 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