The global dimension of the group rings of abelian groups
Stanisław Balcerzyk (1964)
Fundamenta Mathematicae
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Displaying similar documents to “The homological dimension of a torsion-free abelian group of finite rank as a module over its ring of endomorphisms”
The global dimension of the group rings of abelian groups
Torsion-free modules and syzygies.
Katz, D. (1994)
Mathematica Pannonica
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Some torsion theoretical characterizations of rings.
Ahsan, Javed (1984)
International Journal of Mathematics and Mathematical Sciences
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Torsion-free abelian groups and completely decomposable -adic modules
G. d'Este (1980)
Rendiconti del Seminario Matematico della Università di Padova
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The global dimension of the group rings of abelian groups II
Stanisław Balcerzyk (1966)
Fundamenta Mathematicae
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Hulls of mixed modules with finite quotient -rank
Otto Mutzbauer, Elias Toubassi (1999)
Czechoslovak Mathematical Journal
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Extensionless modules over tame hereditary algebras
Frank Okoh (1997)
Colloquium Mathematicae
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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].