Finite and infinite collections of multiplication modules.
Ali, Majid M., Smith, David J. (2001)
Beiträge zur Algebra und Geometrie
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Ali, Majid M., Smith, David J. (2001)
Beiträge zur Algebra und Geometrie
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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].
Andrzej Tyc (1998)
Colloquium Mathematicae
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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...
Ali, Majid M., Smith, David J. (2004)
Beiträge zur Algebra und Geometrie
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Bonanzinga, Vittoria, Restuccia, Gaetana (2002)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Singh, Surjeet, Al-Bleehed, Hind (2004)
Beiträge zur Algebra und Geometrie
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Wisbauer, Robert, Yousif, Mohamed F., Zhou, Yiqiang (2002)
Beiträge zur Algebra und Geometrie
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Puthenpurakal, Tony J. (2005)
Beiträge zur Algebra und Geometrie
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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...
Ali, Majid M. (2006)
Beiträge zur Algebra und Geometrie
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Oneto R., Ángel V. (1996)
Divulgaciones Matemáticas
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