Name
Title | ||
|---|---|---|
Rank Of Submodule, Linear Transformations And Linearly Independent Subsets Of Z-Module |
Abstract | ||
|---|---|---|
In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, and that there exists a submodule with any given rank that satisfies the above condition. In the next section, we mention basic facts of linear transformations between two Z-modules. In this section, we define homomorphism between two Z-modules and deal with kernel and image of homomorphism. In the last section, we formally prove some basic facts about linearly independent subsets and linear combinations. These formalizations are based on [9](p.191-242), [23](p.117-172) and [2](p.17-35). |
Year | DOI | Venue |
|---|---|---|
2014 | 10.2478/forma-2014-0021 | FORMALIZED MATHEMATICS |
Keywords | Field | DocType |
free Z-module, rank of Z-module, homomorphism of Z-module, linearly independent, linear combination | Rank (linear algebra),Kernel (linear algebra),Linear combination,Discrete mathematics,Linear independence,Free module,Linear map,Homomorphism,Mathematics,Module | Journal |
Volume | Issue | ISSN |
22 | 3 | 1898-9934 |
Citations | PageRank | References |
1 | 0.43 | 4 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kazuhisa Nakasho | 1 | 7 | 8.59 |
| Yuichi Futa | 2 | 23 | 15.08 |
| Hiroyuki Okazaki | 3 | 2 | 5.31 |
| Yasunari Shidama | 4 | 166 | 72.47 |