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QUELQUES TENTATIVES DE DÉFINIR UNE NOTION GÉNÉRALE DE GROUPES ET DE CORPS DE DIMENSION UN ET DE DÉTERMINER LEURS PROPRIÉTÉS ALGÉBRIQUES

BRUNO POIZAT

Université de Lyon, CNRS Université Lyon 1, INSA de Lyon, Ecole Centrale de Lyon, Institut Camille Jordan UMR5208, 21 avenue Claude Bernard, F-69622 Villeurbanne-cedex, France

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https://doi.org/10.1142/S1793744209000043Cited by:3 (Source: Crossref)

Abstract

We make some attempts to define a general notion of groups and fields of dimension one, and to determine their algebraic properties.

Keywords:

AMSC: 20A15, 20E34, 03C50, 03C60

References

C. Berline and D. Lascar, Ann. Pure Appl. Logic 30, 1 (1986), DOI: 10.1016/0168-0072(86)90035-7. Crossref, Google Scholar
G. Cherlin, Superstable Division Rings (North-Holland, 1978) pp. 99–111. Google Scholar
G. Cherlin, Ann. Pure Appl. Logic 17, 1 (1979). Google Scholar
G. Cherlin, J. Groups Th. 8, 613 (2005), DOI: 10.1515/jgth.2005.8.5.613. Google Scholar
G. Cherlin , T. Altinel and A. Borovik , Simple Groups of Finite Morley Rank of Even Type ( Amer. Math. Soc. , 2008 ) . Google Scholar
C. Ealy and A. Onshus, J. Symbolic Logic 72, 919 (2007), DOI: 10.2178/jsl/1191333848. Crossref, Google Scholar
M. Herzog, P. Longobardi and M. Maj, J. Group Th. 11, 105 (2008), DOI: 10.1515/JGT.2008.007. Google Scholar
A. Macintyre, Fund. Math. 71, 1 (1971). Crossref, Google Scholar
B. H. Neumann, J. London Math. Soc. 29, 236 (1954). Google Scholar
A. Ol'shanskii, Alg. Logika 21, 553 (1982). Google Scholar
A. Pillay and B. Poizat, J. Symbolic Logic 60, 528 (1995). Crossref, Google Scholar
B. Poizat , Cours de Théorie des Modèles ( Nur al-Mantiq wal-Ma'rifah , 1985 ) . Google Scholar
B. Poizat , Groupes Stables ( Nur al-Mantiq wal-Ma'rifah , 1987 ) . Google Scholar
B. Poizat, J. Symbolic Logic 66, 1637 (2001). Crossref, Google Scholar
J. Reineke, Z. Math. Logik 21, 357 (1975). Crossref, Google Scholar
F. O. Wagner, J. Symbolic Logic 65, 1833 (2000). Crossref, Google Scholar
F. O. Wagner, J. Symbolic Logic 66, 703 (2001). Crossref, Google Scholar
F. O. Wagner, Bull. London Math. Soc. 35, 499 (2003), DOI: 10.1112/S0024609303001929. Crossref, Google Scholar
F. O. Wagner, Groups in simple theories, Logic Colloquium 2001, Lecture Notes in Logic, Vol. 20 (Association for Symbolic Logic, 2005), pp. 440–467 . Google Scholar