The growth of Iwasawa invariants in a family
Albert A. Cuoco (1980)
Compositio Mathematica
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Albert A. Cuoco (1980)
Compositio Mathematica
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John Coates, Takako Fukaya, Kazuya Kato, Ramdorai Sujatha, Otmar Venjakob (2005)
Publications Mathématiques de l'IHÉS
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Let G be a compact -adic Lie group, with no element of order , and having a closed normal subgroup H such that G/H is isomorphic to . We prove the existence of a canonical Ore set S of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient...
Franjou, Vincent, van der Kallen, Wilberd (2010)
Documenta Mathematica
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Bjorn Poonen (1995)
Compositio Mathematica
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Kenkichi Iwasawa (1972)
Acta Arithmetica
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John Coates (2001-2002)
Séminaire Bourbaki
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Kay Wingberg (1985)
Compositio Mathematica
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L. Fuchs, L. Salce (1988)
Rendiconti del Seminario Matematico della Università di Padova
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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]. ...