Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992 Association of Mizar Users

Submodules


Michal Muzalewski
Warsaw University, Bialystok

Summary.

This article contains the notions of trivial and non-trivial leftmodules and rings, cyclic submodules and inclusion of submodules. A few basic theorems related to these notions are proved.

MML Identifier: LMOD_6

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

Contents (PDF format)

  1. Preliminaries
  2. Trivial and non-trivial modules and rings
  3. Submodules and subsets
  4. Cyclic submodules
  5. Inclusion of left R-modules

Bibliography

[1] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[3] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[4] Michal Muzalewski. Free modules. Journal of Formalized Mathematics, 3, 1991.
[5] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[6] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[7] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[8] Wojciech A. Trybulec. Linear combinations in vector space. Journal of Formalized Mathematics, 2, 1990.
[9] Wojciech A. Trybulec. Operations on subspaces in vector space. Journal of Formalized Mathematics, 2, 1990.
[10] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Journal of Formalized Mathematics, 2, 1990.
[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[12] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received June 19, 1992


[ Download a postscript version, MML identifier index, Mizar home page]