# Isomorphism Theorem on Vector Spaces over a Ring

Formalized Mathematics (2017)

- Volume: 25, Issue: 3, page 171-178
- ISSN: 1426-2630

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topYuichi 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 -

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