Submodule of free Z-module

Yuichi Futa; Hiroyuki Okazaki; Yasunari Shidama

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Displaying similar documents to “Submodule of free Z-module”

Z-modules

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

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In this article, we formalize Z-module, that is a module over integer ring. Z-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm and cryptographic systems with lattices [11].

Quotient Module of Z-module

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

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In this article we formalize a quotient module of Z-module and a vector space constructed by the quotient module. We formally prove that for a Z-module V and a prime number p, a quotient module V/pV has the structure of a vector space over Fp. Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattices [14]. Some theorems in this article are described by translating theorems in [20] and [19] into theorems...

An elementary proof of the Weitzenböck Theorem

Andrzej Tyc (1998)

Colloquium Mathematicae

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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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Almost free splitters

Rüdiger Göbel, Saharon Shelah (1999)

Colloquium Mathematicae

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Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that $E x t_{R} (G, G) = 0$ . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which...