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AuthorFerrero, Celestina Cotti. author
TitleNearrings [electronic resource] : Some Developments Linked to Semigroups and Groups / by Celestina Cotti Ferrero, Giovanni Ferrero
ImprintBoston, MA : Springer US, 2002
Connect tohttp://dx.doi.org/10.1007/978-1-4613-0267-4
Descript XX, 611 p. online resource

SUMMARY

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 s̀impler' 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


CONTENT

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 Hersteinโ{128}{153}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 Grรถnewald and Olivier -- 5.6 A generalization of primary Nรถther decomposition -- 5.7 Minimal ideals -- 6. โ{128}{156}Simplerโ{128}{157} 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


Mathematics Coding theory Computer science -- Mathematics Associative rings Rings (Algebra) Group theory Combinatorics Mathematics Associative Rings and Algebras Combinatorics Discrete Mathematics in Computer Science Group Theory and Generalizations Coding and Information Theory



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