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The Endomorphism Monoid of the Random Graph has Uncountably Many Ideals

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Abstract

In this note we prove that the monoid End(R) of all endomorphisms of the random graph R is not simple. On the contrary, the lattice of ideals of End(R) embeds the poset of all subsets of ω, the set of natural numbers.

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Authors and Affiliations

  1. Department of Mathematics, Physics, and Computer Science, Ryerson University, 350 Victoria Street, Toronto, ON M5B 2K3, Canada

    Dejan Delic

  2. Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovica 4 21000 Novi Sad, Serbia and Montenegro

    Igor Dolinka

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  1. Dejan Delic
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  2. Igor Dolinka
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Correspondence to Dejan Delic or Igor Dolinka.

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Delic, D., Dolinka, I. The Endomorphism Monoid of the Random Graph has Uncountably Many Ideals. Semigroup Forum 69, 75–79 (2004). https://doi.org/10.1007/s00233-004-0118-0

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  • DOI: https://doi.org/10.1007/s00233-004-0118-0

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