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Coset laws for categorical skew lattices

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Abstract

During the last three decades, skew lattices proved to be the most successful noncommutative generalization of lattices. In recent times, the study of categorical skew lattices has revealed its importance, especially in the context of several recent investigations of distributivity and cancellation for skew lattices. In this work, we present several characterizations for categorical skew lattices, as well as the description of its coset structure through the study of coset bijections. Several relevant combinatorial results are consequences of this characterization.

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Authors and Affiliations

  1. Mathematics Department, University of Ljubljana, Ljubljana, Slovenia

    João Pita Costa

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  1. João Pita Costa
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Correspondence to João Pita Costa.

Additional information

Presented by M. Jackson.

The author thanks Fundação para a Ciência e Tecnologia, ref. SFRH/BD/36694/2007 for support.

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Pita Costa, J. Coset laws for categorical skew lattices. Algebra Univers. 68, 75–89 (2012). https://doi.org/10.1007/s00012-012-0194-z

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  • DOI: https://doi.org/10.1007/s00012-012-0194-z

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