Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
Free Modules
-
Michal Muzalewski
-
Warsaw University, Bialystok
Summary.
-
We define free modules and prove that every left module over
Skew-Field is free.
MML Identifier:
MOD_3
The terminology and notation used in this paper have been
introduced in the following articles
[10]
[5]
[17]
[6]
[2]
[18]
[3]
[4]
[11]
[12]
[1]
[13]
[7]
[8]
[16]
[15]
[14]
[9]
Contents (PDF format)
Bibliography
- [1]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
- [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
- [3]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
- [8]
Michal Muzalewski.
Construction of rings and left-, right-, and bi-modules over a ring.
Journal of Formalized Mathematics,
2, 1990.
- [9]
Michal Muzalewski and Wojciech Skaba.
Linear independence in left module over domain.
Journal of Formalized Mathematics,
2, 1990.
- [10]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [11]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
Journal of Formalized Mathematics,
2, 1990.
- [12]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
- [13]
Wojciech A. Trybulec.
Linear combinations in real linear space.
Journal of Formalized Mathematics,
2, 1990.
- [14]
Wojciech A. Trybulec.
Linear combinations in vector space.
Journal of Formalized Mathematics,
2, 1990.
- [15]
Wojciech A. Trybulec.
Operations on subspaces in vector space.
Journal of Formalized Mathematics,
2, 1990.
- [16]
Wojciech A. Trybulec.
Subspaces and cosets of subspaces in vector space.
Journal of Formalized Mathematics,
2, 1990.
- [17]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [18]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received October 18, 1991
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