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Article Dans Une Revue The Journal of Symbolic Logic Année : 2013

Fields with few types

Résumé

Let R be an associative ring with possible extra structure. R is said to be weakly small if there are countably many 1-types over any finite subset of R. It is locally P if the algebraic closure of any finite subset of R has property P. It is shown here that a field extension of finite degree of a weakly small field either is a finite field or has no Artin-Schreier extension. A weakly small field of characteristic 2 is finite or algebraically closed. Every weakly small division ring of positive characteristic is locally finite dimensional over its centre. The Jacobson radical of a weakly small ring is locally nilpotent. Every weakly small division ring is locally, modulo its Jacobson radical, isomorphic to a product of finitely many matrix rings over division rings.
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Dates et versions

hal-00582392 , version 1 (01-04-2011)

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Cédric Milliet. Fields with few types. The Journal of Symbolic Logic, 2013, 78 (01), pp.72-84. ⟨10.2178/jsl.7801050⟩. ⟨hal-00582392⟩
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