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The lattice of convexities of partial monounary algebras

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Abstract

A class of partial monounary algebras is called a convexity if it is closed under homomorphic images, direct products and convex relative subalgebras. We prove that the collection of all convexities of partial monounary algebras forms a countable set. Further, each convexity can be generated by at most two algebras.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Science, Pavol Jozef Šafárik University in Košice, Jesenná 5, 041 54, Kosice, Slovakia

    Miroslava Černegová & Danica Jakubíková-Studenovská

Authors
  1. Miroslava Černegová
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  2. Danica Jakubíková-Studenovská
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Corresponding author

Correspondence to Danica Jakubíková-Studenovská.

Additional information

Presented by R. Pöschel.

This article is dedicated to Bjarni Jónsson.

This article is part of the topical collection “In memory of Bjarni Jónsson” edited by J. B. Nation.

This work was supported by the Grants VEGA 1/0063/14 and VEGA 1/0097/18.

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Černegová, M., Jakubíková-Studenovská, D. The lattice of convexities of partial monounary algebras. Algebra Univers. 79, 10 (2018). https://doi.org/10.1007/s00012-018-0492-1

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  • DOI: https://doi.org/10.1007/s00012-018-0492-1

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