Name
Abstract | ||
|---|---|---|
In this article, we formalize a torsion Z-module and a torsion-free Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lovasz) base reduction algorithm [20], cryptographic systems with lattice [21], and coding theory [11]. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.2478/forma-2014-0028 | FORMALIZED MATHEMATICS |
Keywords | Field | DocType |
free Z-module, rank of Z-module, homomorphism of Z-module, linearly independent, linear combination | Linear combination,Discrete mathematics,Linear independence,Free module,Finitely-generated abelian group,Lattice (order),Torsion (mechanics),Rank of an abelian group,Module,Mathematics | Journal |
Volume | Issue | ISSN |
22 | 4 | 1898-9934 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuichi Futa | 1 | 23 | 15.08 |
| Hiroyuki Okazaki | 2 | 2 | 5.31 |
| Kazuhisa Nakasho | 3 | 7 | 8.59 |
| Yasunari Shidama | 4 | 166 | 72.47 |