The lattice R-tors for perfect rings.
H. A. Rincón Mejía (1989)
Publicacions Matemàtiques
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H. A. Rincón Mejía (1989)
Publicacions Matemàtiques
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Ahsan, J., Enochs, E. (1981)
Portugaliae mathematica
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Mark L. Teply, Blas Torrecillas (1993)
Czechoslovak Mathematical Journal
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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].
Seog Hoon Rim, Mark L. Teply (1998)
Czechoslovak Mathematical Journal
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Henderson, J., Orzech, M. (1977)
Portugaliae mathematica
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