Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

Prime Ideals and Filters


Grzegorz Bancerek
Warsaw University, Bialystok

Summary.

The part of [11, pp. 73-77], i.e. definitions and propositions 3.16-3.27, is formalized in the paper.

This work has been partially supported by the Office of Naval Research Grant N00014-95-1-1336.

MML Identifier: WAYBEL_7

The terminology and notation used in this paper have been introduced in the following articles [20] [8] [22] [17] [23] [24] [7] [10] [6] [18] [14] [19] [1] [21] [2] [3] [4] [13] [9] [15] [5] [16] [12]

Contents (PDF format)

  1. The lattice of subsets
  2. Prime ideals and filters
  3. Cluster points of a filter of sets
  4. Pseudo prime elements

Bibliography

[1] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[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] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[10] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[11] 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.
[12] Adam Grabowski. Auxiliary and approximating relations. Journal of Formalized Mathematics, 8, 1996.
[13] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[14] Zbigniew Karno. Maximal discrete subspaces of almost discrete topological spaces. Journal of Formalized Mathematics, 5, 1993.
[15] Artur Kornilowicz. Cartesian products of relations and relational structures. Journal of Formalized Mathematics, 8, 1996.
[16] Beata Madras. Irreducible and prime elements. Journal of Formalized Mathematics, 8, 1996.
[17] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[18] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[19] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.
[20] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[21] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[22] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[23] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[24] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received December 1, 1996


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