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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