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]
-
Preliminaries
-
Trivial and non-trivial modules and rings
-
Submodules and subsets
-
Cyclic submodules
-
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
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