algebra universalis

, Volume 38, Issue 3, pp 235–237 | Cite as

On the least complete extension of complete subsemilattices

  • R. Giacobazzi
  • F. Ranzato


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.


Positive Answer Complete Lattice Complete Extension Complete Sublattice 
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Copyright information

© Birkhäuser Verlag Basel, 1997

Authors and Affiliations

  • R. Giacobazzi
    • 1
  • F. Ranzato
    • 2
  1. 1.Dipartimento di Informatica, Università di Pisa, Corso Italia 40, I-56125 Pisa, Italy. E-mail: giaco@di.unipi.itIT
  2. 2.Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, I-35131 Padova, Italy. E-mail: franz@math.unipd.itIT

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