Small skew fields

Cédric Milliet (1, 2)

1 ICJ - Institut Camille Jordan
2 Département de Mathématiques

Wedderburn showed in 1905 that finite fields are commutative. As for infinite fields, we know that superstable (Cherlin, Shelah) and supersimple (Pillay, Scanlon, Wagner) ones are commutative. In their proof, Cherlin and Shelah use the fact that a superstable field is algebraically closed. Wagner showed that a small field is algebraically closed , and asked whether a small field should be commutative. We shall answer this question positively in non-zero characteristic.

Mots clés: Smallness; skew fields

Domaines: Logique [math.LO]

Cédric Milliet. Small skew fields. Mathematical Logic Quarterly, 2007, 53 (1), pp.86-90. ⟨10.1002/malq.200610029⟩. ⟨hal-00582393⟩