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.