Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993 Association of Mizar Users

Domains of Submodules, Join and Meet of Finite Sequences of Submodules and Quotient Modules


Michal Muzalewski
Warsaw University, Bialystok

Summary.

Notions of domains of submodules, join and meet of finite sequences of submodules and quotient modules. A few basic theorems and schemes related to these notions are proved.

MML Identifier: LMOD_7

The terminology and notation used in this paper have been introduced in the following articles [13] [5] [18] [3] [4] [2] [1] [12] [19] [11] [14] [6] [7] [17] [16] [15] [10] [8] [9]

Contents (PDF format)

  1. Schemes
  2. Auxiliary theorems on free-modules
  3. Domains of submodules
  4. Join and meet of finite sequences of submodules
  5. Sum of subsets of module
  6. Vector of subset
  7. Quotient modules

Bibliography

[1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[6] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[7] Michal Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Journal of Formalized Mathematics, 2, 1990.
[8] Michal Muzalewski. Free modules. Journal of Formalized Mathematics, 3, 1991.
[9] Michal Muzalewski. Submodules. Journal of Formalized Mathematics, 4, 1992.
[10] Michal Muzalewski and Wojciech Skaba. Linear independence in left module over domain. Journal of Formalized Mathematics, 2, 1990.
[11] Michal Muzalewski and Wojciech Skaba. Three-argument operations and four-argument operations. Journal of Formalized Mathematics, 2, 1990.
[12] Andrzej Trybulec. Semilattice operations on finite subsets. Journal of Formalized Mathematics, 1, 1989.
[13] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[14] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[15] Wojciech A. Trybulec. Linear combinations in vector space. Journal of Formalized Mathematics, 2, 1990.
[16] Wojciech A. Trybulec. Operations on subspaces in vector space. Journal of Formalized Mathematics, 2, 1990.
[17] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Journal of Formalized Mathematics, 2, 1990.
[18] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[19] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received March 29, 1993

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