Ideal clones: Solution to a problem of Czedli and Heindorf

Details Ideal clones: Solution to a problem of Czedli and Heindorf Ideal clones: Solution to a problem of Czedli and Heindorf

2008-05-05

arxiv.org/abs/0805.0551v2

Mathematics

Rings and Algebras

9 pages. Changes for version 2: Now the references work (hopefully)

Scientific paper

Given an infinite set X and an ideal I of subsets of X, the set of all finitary operations on X which map all (powers of) I-small sets to I-small sets is a clone. In a 2001 article, G. Czedli and L. Heindorf asked whether or not for two particular ideals I and J on a countably infinite set X, the corresponding ideal clones were a covering in the lattice of clones. We give an affirmative answer to this question.

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