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Natural congruences and isomorphism theorems for directed complete partially ordered sets

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Abstract

Directed complete partially ordered sets (dcpos, for short) play an important role in domain theory. The aim of this paper is to characterise natural congruences of dcpos. We also show that the kernels of dcpo maps, that is, directed join-preserving maps between dcpos are not necessarily natural dcpo congruences. Then we characterise dcpo maps whose kernels are natural dcpo congruences. Finally, we prove the Decomposition and Isomorphism Theorems for dcpo maps.

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Authors and Affiliations

  1. Department of Mathematics, Shahid Beheshti University, G.C., Tehran, 19839, Iran

    Mojgan Mahmoudi

  2. Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran

    Halimeh Moghbeli

  3. Department of Mathematics, Shahid Beheshti University, Tehran, 19839, Iran

    Halimeh Moghbeli

  4. Institute of Mathematics, University of Warsaw, ul. Banacha 2, Warsaw, PL-02-097, Poland

    Konrad Pióro

Authors
  1. Mojgan Mahmoudi
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  2. Halimeh Moghbeli
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  3. Konrad Pióro
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Corresponding author

Correspondence to Mojgan Mahmoudi.

Additional information

Presented by J. Adamek.

The first author would like to thank the Institute of Mathematics of the University of Warsaw for their kind hospitality during her stay on October 2013, also sincerely thanks SALAM representatives and coordinators in both home and host university for receiving scholarship under the Erasmus Mundus project.

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Mahmoudi, M., Moghbeli, H. & Pióro, K. Natural congruences and isomorphism theorems for directed complete partially ordered sets. Algebra Univers. 77, 79–99 (2017). https://doi.org/10.1007/s00012-017-0424-5

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  • DOI: https://doi.org/10.1007/s00012-017-0424-5

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