Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

On the Characterization of Modular and Distributive Lattices


Adam Naumowicz
University of Bialystok

Summary.

This article contains definitions of the ``pentagon'' lattice $N_5$ and the ``diamond'' lattice $M_3$. It is followed by the characterization of modular and distributive lattices depending on the possible shape of substructures. The last part treats of interval-like sublattices of any lattice.

This work has been supported by KBN Grant 8 T11C 018 12.

MML Identifier: YELLOW11

The terminology and notation used in this paper have been introduced in the following articles [11] [10] [13] [14] [5] [6] [12] [2] [3] [9] [15] [7] [8] [4] [1]

Contents (PDF format)

  1. Preliminaries
  2. Main Part
  3. Diamond and Pentagon
  4. Intervals of a Lattice

Bibliography

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[4] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
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[6] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
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[8] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
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[11] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[12] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[13] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[14] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[15] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received April 3, 1998

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