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

Completely-Irreducible Elements


Robert Milewski
University of Bialystok

Summary.

The article is a translation of [9, 92-93].

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

MML Identifier: WAYBEL16

The terminology and notation used in this paper have been introduced in the following articles [19] [6] [21] [16] [22] [8] [5] [18] [20] [17] [1] [2] [11] [12] [3] [7] [13] [4] [10] [14] [15]

Contents (PDF format)

  1. Preliminaries
  2. Free Generation Set
  3. Completely-Irreducible Elements

Bibliography

[1] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[2] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.
[3] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[4] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[5] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[8] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[9] 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.
[10] Adam Grabowski. Auxiliary and approximating relations. Journal of Formalized Mathematics, 8, 1996.
[11] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[12] Artur Kornilowicz. Definitions and properties of the join and meet of subsets. Journal of Formalized Mathematics, 8, 1996.
[13] Artur Kornilowicz. Meet -- continuous lattices. Journal of Formalized Mathematics, 8, 1996.
[14] Beata Madras. Irreducible and prime elements. Journal of Formalized Mathematics, 8, 1996.
[15] Robert Milewski. Algebraic lattices. Journal of Formalized Mathematics, 8, 1996.
[16] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[17] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[18] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[19] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[20] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received February 9, 1998


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