Isomorphism Theorem on Vector Spaces over a Ring

Yuichi Futa, and Yasunari Shidama. "Isomorphism Theorem on Vector Spaces over a Ring." Formalized Mathematics 25.3 (2017): 171-178. <http://eudml.org/doc/288337>.

@article{YuichiFuta2017,
abstract = {In this article, we formalize in the Mizar system [1, 4] some properties of vector spaces over a ring. We formally prove the first isomorphism theorem of vector spaces over a ring. We also formalize the product space of vector spaces. ℤ-modules are useful for lattice problems such as LLL (Lenstra, Lenstra and Lovász) [5] base reduction algorithm and cryptographic systems [6, 2].},
author = {Yuichi Futa, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {isomorphism theorem; vector space},
language = {eng},
number = {3},
pages = {171-178},
title = {Isomorphism Theorem on Vector Spaces over a Ring},
url = {http://eudml.org/doc/288337},
volume = {25},
year = {2017},
}

TY - JOUR
AU - Yuichi Futa
AU - Yasunari Shidama
TI - Isomorphism Theorem on Vector Spaces over a Ring
JO - Formalized Mathematics
PY - 2017
VL - 25
IS - 3
SP - 171
EP - 178
AB - In this article, we formalize in the Mizar system [1, 4] some properties of vector spaces over a ring. We formally prove the first isomorphism theorem of vector spaces over a ring. We also formalize the product space of vector spaces. ℤ-modules are useful for lattice problems such as LLL (Lenstra, Lenstra and Lovász) [5] base reduction algorithm and cryptographic systems [6, 2].
LA - eng
KW - isomorphism theorem; vector space
UR - http://eudml.org/doc/288337
ER -