### Weak baer modules localized with respect to a torsion theory

Seog Hoon Rim, Mark L. Teply (1998)

Czechoslovak Mathematical Journal

Similarity:

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Seog Hoon Rim, Mark L. Teply (1998)

Czechoslovak Mathematical Journal

Similarity:

M. Rauf Quershi (1973)

Fundamenta Mathematicae

Similarity:

Mark L. Teply, Blas Torrecillas (1993)

Czechoslovak Mathematical Journal

Similarity:

Henderson, J., Orzech, M. (1977)

Portugaliae mathematica

Similarity:

László Fuchs, Rüdiger Göbel (2007)

Rendiconti del Seminario Matematico della Università di Padova

Similarity:

Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho, Yasunari Shidama (2014)

Formalized Mathematics

Similarity:

In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lov´asz) base reduction algorithm [20], cryptographic systems with lattice [21], and coding theory [11].

Wang, Yongduo (2005)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Yuichi Futa, Yasunari Shidama (2016)

Formalized Mathematics

Similarity:

In this article, we formalize the definition of divisible ℤ-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible ℤ-modules are not finitely-generated.We introduce a divisible ℤ-module, equivalent to a vector space of a torsion-free ℤ-module with a coefficient ring ℚ. ℤ-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [15], cryptographic systems with lattices [16] and coding theory [8]. ...