Three Notes on Distributive Lattices

@article{Wild1998ThreeNO,
  title={Three Notes on Distributive Lattices},
  author={Marcel Wild},
  journal={Advances in Applied Mathematics},
  year={1998},
  volume={20},
  pages={44-49}
}
  • M. Wild
  • Published 1998
  • Mathematics
  • Advances in Applied Mathematics
The present paper comprises three rather independent notes. The first and second notes are about finite distributive lattices. We hasten to add that the title is a bit unprecise; the third note is actually about finite meet semidistributive lattices. In Section 1 an example of a self-dual distributive lattice, which does not allow for a polarity is given. This answers a question of Kamara. Another question of Metropolis, Rota, and Stein is settled as well. Both problems fit well into the… 
On L-Tychonoff spaces II
Involutive Residuated Lattices Based on Modular and Distributive Lattices
TLDR
It is shown that a large class of self-dual lattices may be endowed with an IRL structure, and examples of lattices which fail to admit IRLs with natural algebraic conditions are given.

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