Volume 5, 1993

University of Bialystok

Copyright (c) 1993 Association of Mizar Users

**Michal Muzalewski**- Warsaw University, Bialystok

- Notions of domains of submodules, join and meet of finite sequences of submodules and quotient modules. A few basic theorems and schemes related to these notions are proved.

- Schemes
- Auxiliary theorems on free-modules
- Domains of submodules
- Join and meet of finite sequences of submodules
- Sum of subsets of module
- Vector of subset
- Quotient modules

- [1]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Czeslaw Bylinski.
Binary operations.
*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]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Michal Muzalewski.
Construction of rings and left-, right-, and bi-modules over a ring.
*Journal of Formalized Mathematics*, 2, 1990. - [8]
Michal Muzalewski.
Free modules.
*Journal of Formalized Mathematics*, 3, 1991. - [9]
Michal Muzalewski.
Submodules.
*Journal of Formalized Mathematics*, 4, 1992. - [10]
Michal Muzalewski and Wojciech Skaba.
Linear independence in left module over domain.
*Journal of Formalized Mathematics*, 2, 1990. - [11]
Michal Muzalewski and Wojciech Skaba.
Three-argument operations and four-argument operations.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Andrzej Trybulec.
Semilattice operations on finite subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [14]
Wojciech A. Trybulec.
Vectors in real linear space.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Wojciech A. Trybulec.
Linear combinations in vector space.
*Journal of Formalized Mathematics*, 2, 1990. - [16]
Wojciech A. Trybulec.
Operations on subspaces in vector space.
*Journal of Formalized Mathematics*, 2, 1990. - [17]
Wojciech A. Trybulec.
Subspaces and cosets of subspaces in vector space.
*Journal of Formalized Mathematics*, 2, 1990. - [18]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [19]
Stanislaw Zukowski.
Introduction to lattice theory.
*Journal of Formalized Mathematics*, 1, 1989.

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