%0 Journal Article
%T Z-modules
%A Yuichi Futa
%A Hiroyuki Okazaki
%A Yasunari Shidama
%J Formalized Mathematics
%@ 1898-9934
%D 2012
%I 
%R 10.2478/v10037-012-0007-z
%X In this article, we formalize Z-module, that is a module over integer ring. Z-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lov¨¢sz) base reduction algorithm and cryptographic systems with lattices [11].
%U http://versita.metapress.com/content/53520r01335v0138/?p=430716bb19384440aaea6ce45ed7408d&pi=6