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On the least complete extension of complete subsemilattices

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Abstract.

For a complete sublattice X of a complete lattice C, we consider the problem of the existence of the least complete meet subsemilattice of C having as least complete extension (i.e., the least complete sublattice of C containing it) X. We argue that this problem is not trivial, and we provide two results that, under certain conditions on C and X, give a positive answer to this problem.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Corso Italia 40, I-56125 Pisa, Italy. E-mail: giaco@di.unipi.it, , , , , , IT

    R. Giacobazzi

  2. Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, I-35131 Padova, Italy. E-mail: franz@math.unipd.it, , , , , , IT

    F. Ranzato

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  1. R. Giacobazzi
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  2. F. Ranzato
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Received January 31, 1997; accepted in final form October 23, 1997.

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Giacobazzi, R., Ranzato, F. On the least complete extension of complete subsemilattices. Algebra univers. 38, 235–237 (1997). https://doi.org/10.1007/s000120050053

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  • DOI: https://doi.org/10.1007/s000120050053

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