Algebraic and Arithmetic Lattices. Part II
Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997
Association of Mizar Users
Algebraic and Arithmetic Lattices. Part II
-
Robert Milewski
-
University of Bialystok
Summary.
-
The article is a translation of [10, pp. 89-92].
This work has been supported by
KBN Grant 8 T11C 018 12.
The terminology and notation used in this paper have been
introduced in the following articles
[16]
[18]
[19]
[6]
[7]
[9]
[17]
[15]
[2]
[14]
[1]
[3]
[11]
[21]
[4]
[8]
[5]
[20]
[12]
[13]
-
Preliminaries
-
Maps Preserving Sup's and Inf's
-
Atoms Elements
-
More on the Boolean Lattice
Bibliography
- [1]
Grzegorz Bancerek.
Complete lattices.
Journal of Formalized Mathematics,
4, 1992.
- [2]
Grzegorz Bancerek.
Quantales.
Journal of Formalized Mathematics,
6, 1994.
- [3]
Grzegorz Bancerek.
Bounds in posets and relational substructures.
Journal of Formalized Mathematics,
8, 1996.
- [4]
Grzegorz Bancerek.
Directed sets, nets, ideals, filters, and maps.
Journal of Formalized Mathematics,
8, 1996.
- [5]
Grzegorz Bancerek.
The ``way-below'' relation.
Journal of Formalized Mathematics,
8, 1996.
- [6]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [8]
Czeslaw Bylinski.
Galois connections.
Journal of Formalized Mathematics,
8, 1996.
- [9]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
- [10]
G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott.
\em A Compendium of Continuous Lattices.
Springer-Verlag, Berlin, Heidelberg, New York, 1980.
- [11]
Adam Grabowski and Robert Milewski.
Boolean posets, posets under inclusion and products of relational structures.
Journal of Formalized Mathematics,
8, 1996.
- [12]
Beata Madras.
Irreducible and prime elements.
Journal of Formalized Mathematics,
8, 1996.
- [13]
Robert Milewski.
Algebraic lattices.
Journal of Formalized Mathematics,
8, 1996.
- [14]
Michal Muzalewski.
Categories of groups.
Journal of Formalized Mathematics,
3, 1991.
- [15]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
- [16]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [17]
Wojciech A. Trybulec.
Partially ordered sets.
Journal of Formalized Mathematics,
1, 1989.
- [18]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [19]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [20]
Mariusz Zynel.
The equational characterization of continuous lattices.
Journal of Formalized Mathematics,
8, 1996.
- [21]
Mariusz Zynel and Czeslaw Bylinski.
Properties of relational structures, posets, lattices and maps.
Journal of Formalized Mathematics,
8, 1996.
Received October 29, 1997
[
Download a postscript version,
MML identifier index,
Mizar home page]