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Join congruence relations and closure relations

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Abstract.

In this paper we show that, given a complete lattice \( \mathcal{L} \), the following three lattices are the same: (1) the lattice of closure relations on \( \mathcal{L} \), (2) the lattice of meet-closed subsets of \( \mathcal{L} \), and (3) the lattice of complete join congruence relations on \( \mathcal{L} \).

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Authors and Affiliations

  1. Department of Mathematics, Dartmouth College, 03755, Hanover, NH, USA

    Kenneth P. Bogart & Laura H. Montague

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  1. Kenneth P. Bogart
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  2. Laura H. Montague
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Correspondence to Kenneth P. Bogart.

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Bogart, K.P., Montague, L.H. Join congruence relations and closure relations. Algebra univers. 50, 381–384 (2003). https://doi.org/10.1007/s00012-003-1811-7

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  • DOI: https://doi.org/10.1007/s00012-003-1811-7

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