Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-25T12:11:52.110Z Has data issue: false hasContentIssue false
  • English
  • Français

Quasi-endomorphisms in small stable groups

Published online by Cambridge University Press:  12 March 2014

Frank O. Wagner
Frank O. Wagner*
Affiliation:
Mathematisches Institut, Abteilung für Logik und Grundlagenforschung, Universität Freiburg, Albertstr, 23B, 79104 Freiburg, Deutschland, E-mail: frwagner@ibm.ruf.uni-freiburg.de
Get access Rights & Permissions [Opens in a new window]

Abstract

We generalise various properties of quasiendomorphisms from groups with regular generic to small abelian groups. In particular, for a small stable abelian group such that no infinite definable quotient is connected-by-finite, the ring of quasi-endomorphisms is locally finite. Under some additional assumptions, it decomposes modulo some nil ideal into a sum of finitely many matrix rings.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 3 , September 1993 , pp. 1044 - 1051
Copyright
Copyright © Association for Symbolic Logic 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[B]Buechler, S., Vaught's conjecture for unidimensional theories, preprint.Google Scholar
[HLPTW]Herwig, B., Loveys, J. G., Pillay, A., Tanović, P., and Wagner, F. O., Stable theories without dense forking chains, Archive for Mathematical Logic, vol. 31 (1992), pp. 297–303.CrossRefGoogle Scholar
[HI]Hrushovski, E., Contributions to stable model theory, Ph.D. thesis, University of California, Berkeley, California, 1986.Google Scholar
[H2]Hrushovski, E., Locally modular regular types, Classification theory (Proceedings, Chicago 1985) (Baldwin, J. T., editor), Lecture Notes in Mathematics, vol. 1292, Springer-Verlag, Berlin and New York, 1987, pp. 132–164.CrossRefGoogle Scholar
[Lo]Loveys, J., Abelian groups with modular generic, this Journal, vol. 56 (1991), pp. 250–259.Google Scholar
[P]Pillay, A., Certain locally modular regular superstable groups, preprint.Google Scholar
[PW]Poizat, B. P. and Wagner, F. O., Sous-Groupes périodiques d’un groupe stable, this Journal, vol. 58 (1993), pp. 385–400.Google Scholar
[W1]Wagner, F. O., Small stable groups and generics, this Journal, vol. 56 (1991), pp. 1026–1037.Google Scholar
[W2]Wagner, F. O., More on ℜ, Notre Dame Journal of Formal Logic, vol. 33 (1992), pp. 159–174.Google Scholar