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Divisible ℤ-modules

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Futa Y., Shidama Y.

Formalized Mathematics

2016

tom 24

nr 1

37-47

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].

Ograniczanie wyników

1 Formalized Mathematics

1 Futa Y.

1 Shidama Y.

1 2016

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Divisible ℤ-modules