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The strong endomorphism kernel property for modular p-algebras and for distributive lattices

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Abstract

We study the strong endomorphism kernel property (SEKP) for some classes of universal algebras. Using the Katriňák-Mederly triple construction, we prove a universal equivalent condition under which a modular p-algebra has SEKP. As a consequence, we characterize distributive lattices with top element that enjoy SEKP. Using Priestley duality, we also characterize unbounded distributive lattices that have SEKP.

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Authors and Affiliations

  1. Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Jaroslav Guričan

  2. Faculty of Natural Sciences, Šafárik’s University, Jesenná 5, 04154, Košice, Slovakia

    Miroslav Ploščica

Authors
  1. Jaroslav Guričan
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  2. Miroslav Ploščica
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Correspondence to Jaroslav Guričan.

Additional information

Presented by M. Haviar.

While working on this paper, the first author was supported by VEGA grant No. 1/0608/13 of Slovak Republic, the second author was supported by VEGA grant No. 1/0063/14 of Slovak Republic.

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Guričan, J., Ploščica, M. The strong endomorphism kernel property for modular p-algebras and for distributive lattices. Algebra Univers. 75, 243–255 (2016). https://doi.org/10.1007/s00012-016-0370-7

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  • DOI: https://doi.org/10.1007/s00012-016-0370-7

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