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Some partial results on the cancellation law for the tensor product of complete lattices

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Abstract

In this paper we study the cancellation law for the tensor product in the category \(\mathsf {Sup}\) of complete lattices and join-preserving maps. First, we investigate the tensor product of generalized power-set lattices. Based on which, we prove that the cancellation law for the tensor product has a close relation to that for the cartesian product of posets, and give a class of complete lattices which do not satisfy the cancellation law for the tensor product. Then, we also investigate the cancellation law for particular subclasses of complete lattices.

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Acknowledgements

The authors sincerely thank the anonymous reviewers for their careful inspection and their useful suggestions which improved the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Shaanxi Normal University, Xi’an, 710119, China

    Shengwei Han, Jing Liu & Bin Zhao

  2. Department of Mathematics, University of the Basque Country UPV/EHU, 48080, Bilbao, Spain

    Javier Gutiérrez García

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  1. Shengwei Han
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  2. Jing Liu
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  3. Bin Zhao
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  4. Javier Gutiérrez García
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Correspondence to Shengwei Han.

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The research of the first three authors was supported by the National Natural Science Foundation of China (Grant no. 11971286). The fourth author thanks the Basque Government (Grant IT1483-22).

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Han, S., Liu, J., Zhao, B. et al. Some partial results on the cancellation law for the tensor product of complete lattices. Algebra Univers. 83, 15 (2022). https://doi.org/10.1007/s00012-022-00771-8

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