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Maximal sublattices of finite distributive lattices

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Abstract

Algebraic properties of lattices of quotients of finite posets are considered. Using the known duality between the category of all finite posets together with all order-preserving maps and the category of all finite distributive (0, 1)-lattices together with all (0, 1)-lattice homomorphisms, algebraic and arithmetic properties of maximal proper sublattices and, in particular, Frattini sublattices of finite distributive (0, 1)-lattices are thereby obtained.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, SUNY, 12561, New Paltz, NY, USA

    M. E. Adams

  2. Department of Mathematics, Statistics and Computer Science, University of Illinois, 60607, Chicago, IL, USA

    P. Dwinger

  3. Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland

    J. Schmid

Authors
  1. M. E. Adams
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  2. P. Dwinger
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  3. J. Schmid
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Adams, M.E., Dwinger, P. & Schmid, J. Maximal sublattices of finite distributive lattices. Algebra Universalis 36, 488–504 (1996). https://doi.org/10.1007/BF01233919

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  • DOI: https://doi.org/10.1007/BF01233919

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