Weak baer modules localized with respect to a torsion theory
Seog Hoon Rim, Mark L. Teply (1998)
Czechoslovak Mathematical Journal
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Seog Hoon Rim, Mark L. Teply (1998)
Czechoslovak Mathematical Journal
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M. Rauf Quershi (1973)
Fundamenta Mathematicae
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Mark L. Teply, Blas Torrecillas (1993)
Czechoslovak Mathematical Journal
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Henderson, J., Orzech, M. (1977)
Portugaliae mathematica
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László Fuchs, Rüdiger Göbel (2007)
Rendiconti del Seminario Matematico della Università di Padova
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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].
Wang, Yongduo (2005)
International Journal of Mathematics and Mathematical Sciences
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Yuichi Futa, Yasunari Shidama (2016)
Formalized Mathematics
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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]. ...