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Torsion Part of ℤ-module

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Futa Y., Okazaki H., Shidama Y.

Formalized Mathematics

2015

tom 23

nr 4

297-307

In this article, we formalize in Mizar [7] the definition of “torsion part” of ℤ-module and its properties. We show ℤ-module generated by the field of rational numbers as an example of torsion-free non free ℤ-modules. We also formalize the rank-nullity theorem over finite-rank free ℤ-modules (previously formalized in [1]). ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [23] and cryptographic systems with lattices [24].

Ograniczanie wyników

1 Formalized Mathematics

1 Futa Y.

1 Okazaki H.

1 Shidama Y.

1 2015

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Torsion Part of ℤ-module