Torsion Part of ℤ-module

Yuichi Futa; Hiroyuki Okazaki; Yasunari Shidama

Displaying similar documents to “Torsion Part of ℤ-module”

Torsion Z-module and Torsion-free Z-module

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

Formalized Mathematics

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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].

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M. Rauf Quershi (1973)

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Primary decomposition of torsion $R [X]$ -modules.

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International Journal of Mathematics and Mathematical Sciences

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Extending modules relative to a torsion theory

Semra Doğruöz (2008)

Czechoslovak Mathematical Journal

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An $R$ -module $M$ is said to be an extending module if every closed submodule of $M$ is a direct summand. In this paper we introduce and investigate the concept of a type 2 $τ$ -extending module, where $τ$ is a hereditary torsion theory on $Mod$ - $R$ . An $R$ -module $M$ is called type 2 $τ$ -extending if every type 2 $τ$ -closed submodule of $M$ is a direct summand of $M$ . If $τ_{I}$ is the torsion theory on $Mod$ - $R$ corresponding to an idempotent ideal $I$ of $R$ and $M$ is a type 2 $τ_{I}$ -extending $R$ -module, then the question of whether...