Torsion free exterior powers of a module and their resolutions.

Molica, Giovanni; Restuccia, Gaetana

Displaying similar documents to “Torsion free exterior powers of a module and their resolutions.”

Syzygietic properties of a module and torsion freeness of its symmetric powers.

Bonanzinga, Vittoria, Restuccia, Gaetana (2002)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Torsion Part of ℤ-module

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2015)

Formalized Mathematics

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In this article, we formalize in Mizar [7] the definition of “torsion part” of ℤ-module and its properties. We show ℤ-module generated by the field of rational numbers as an example of torsion-free non free ℤ-modules. We also formalize the rank-nullity theorem over finite-rank free ℤ-modules (previously formalized in [1]). ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [23] and cryptographic systems with lattices [24].

Submodule of free Z-module

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2013)

Formalized Mathematics

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In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems - LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their...

Torsion-free modules and syzygies.

Katz, D. (1994)

Mathematica Pannonica

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Extensionless modules over tame hereditary algebras

Frank Okoh (1997)

Colloquium Mathematicae

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Torsion-free abelian groups and completely decomposable $p$ -adic modules

G. d'Este (1980)

Rendiconti del Seminario Matematico della Università di Padova

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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].