Divisible ℤ-modules
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ID: 97384
2016
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Abstract
In this article, we formalize the definition of divisible ℤ-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible ℤ-modules are not finitely-generated.We introduce a divisible ℤ-module, equivalent to a vector space of a torsion-free ℤ-module with a coefficient ring ℚ. ℤ-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [15], cryptographic systems with lattices [16] and coding theory [8].
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yuichi2016divisibleformalized
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| Authors | Yuichi, Futa;Yasunari, Shidama; |
| Journal | formalized mathematics |
| Year | 2016 |
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