Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-12T02:06:10.003Z Has data issue: false hasContentIssue false
  • English
  • Français

Idempotent ideals on abelian groups

Published online by Cambridge University Press:  12 March 2014

Andrzej Pelc
Andrzej Pelc*
Affiliation:
University of Warsaw, Warsaw, Poland
Get access Rights & Permissions [Opens in a new window]

Abstract

An ideal I defined on a group G is called idempotent if for every A ∈ I, {g ∈ G:Ag−1 ∉ ∈ I} ∈ I. We show that a countably complete idempotent ideal on an abelian group cannot be prime but may have strong saturation properties.

Keywords

Idempotent idealabelian group
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 3 , September 1984 , pp. 813 - 817
Copyright
Copyright © Association for Symbolic Logic 1984

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

[1]Hindman, N., Ultrafilters and combinatorial number theory, Number theory—Carbondale, 1979, Lecture Notes in Mathematics, vol. 751, Springer-Verlag, Berlin, 1979, pp. 119–184.CrossRefGoogle Scholar
[2]Pelc, A., Universal invariant measures and invariant ideals on groups (to appear).Google Scholar
[3]Taylor, A., Some variants of Silver's lemma, manuscript, 1978.Google Scholar