Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Linear Independence in Left Module over Domain
-
Michal Muzalewski
-
Warsaw University, Bialystok
-
Wojciech Skaba
-
Nicolaus Copernicus University, Torun
Summary.
-
Notion of a submodule generated by a set of vectors
and linear independence of a set of vectors. A few theorems originated
as a generalization of the theorems from the article [10].
Supported by RPBP.III-24.C6.
MML Identifier:
LMOD_5
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[14]
[4]
[15]
[2]
[3]
[8]
[1]
[9]
[5]
[6]
[13]
[12]
[11]
Contents (PDF format)
Bibliography
- [1]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
- [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [3]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Michal Muzalewski.
Construction of rings and left-, right-, and bi-modules over a ring.
Journal of Formalized Mathematics,
2, 1990.
- [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [8]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
Journal of Formalized Mathematics,
2, 1990.
- [9]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
- [10]
Wojciech A. Trybulec.
Basis of vector space.
Journal of Formalized Mathematics,
2, 1990.
- [11]
Wojciech A. Trybulec.
Linear combinations in vector space.
Journal of Formalized Mathematics,
2, 1990.
- [12]
Wojciech A. Trybulec.
Operations on subspaces in vector space.
Journal of Formalized Mathematics,
2, 1990.
- [13]
Wojciech A. Trybulec.
Subspaces and cosets of subspaces in vector space.
Journal of Formalized Mathematics,
2, 1990.
- [14]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [15]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received October 22, 1990
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