Torsion Part of Z-module

نویسندگان

  • Yuichi Futa
  • Hiroyuki Okazaki
  • Yasunari Shidama
چکیده

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].

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تاریخ انتشار 2016