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.III24.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 bimodules 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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