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Idempotent ideals on abelian groups

Published online by Cambridge University Press:  12 March 2014

Andrzej Pelc
Andrzej Pelc*
Affiliation:
University of Warsaw, Warsaw, Poland
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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

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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