On almost-free modules over complete discrete valuation rings
R. Göbel, B. Goldsmith (1991)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
R. Göbel, B. Goldsmith (1991)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
Lorenzo Robbiano (1979)
Compositio Mathematica
Similarity:
Katz, D. (1994)
Mathematica Pannonica
Similarity:
Wolfson, Kenneth G. (1990)
Portugaliae mathematica
Similarity:
David A. Buchsbaum (1974-1975)
Séminaire Dubreil. Algèbre et théorie des nombres
Similarity:
Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2012)
Formalized Mathematics
Similarity:
In this article we formalize a free ℤ-module and its rank. We formally prove that for a free finite rank ℤ-module V , the number of elements in its basis, that is a rank of the ℤ-module, is constant regardless of the selection of its basis. ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [15]. Some theorems in this article are described by translating theorems in [21] and [8] into theorems of...
Antonio García Rodicio (1991)
Extracta Mathematicae
Similarity:
Let (A,M,K) denote a local noetherian ring A with maximal ideal M and residue field K. Let I be an ideal of A and E the Koszul complex generated over A by a system of generators of I.
The condition: H1(E) is a free A/I-module, appears in several important results of Commutative Algebra. For instance:
- (Gulliksen [3, Proposition 1.4.9]): The ideal I is generated by a regular sequence if and only if I has finite projective dimension and H
Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho, Yasunari Shidama (2014)
Formalized Mathematics
Similarity:
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].