Tight closure and strong F-regularity
Tight closure and the Kodaira Vanishing Theorem.
Tight closure of an ideal generated by an R-sequence.
Tight closure of parameter ideals.
Tissus du plan et polynômes de Darboux
Dans cet article, nous étudions le problème de l’existence de polynômes de Darboux dans pour la dérivation .
Topological characterizations of ordered groups with quasi-divisor theory
For an order embedding of a partly ordered group into an -group a topology is introduced on which is defined by a family of valuations on . Some density properties of sets , and ( being -ideals in ) in the topological space are then investigated, each of them being equivalent to the statement that is a strong theory of quasi-divisors.
Topological computation of local cohomology multiplicities.
We express the Lyubeznik numbers of the local ring of a complex isolated singularity in terms of Betti numbers of the associated real link.
Topological localization in Fréchet algebras.
Topological -adic vector spaces and index theory
Topological rings that generalize artinian rings.
Topologies de corps A-linéaires
Topologies linéaires et modules absolument purs
Topologies linéaires sur certains anneaux de dimension 1
Topologische Charakterisierung globaler Körper und algebraischer Funktionenkörper in einer Variablen.
Toric varieties in phylogenetics [Book]
Torsion äußerer Potenzen von Moduln der homologischen Dimension l.
Torsion free exterior powers of a module and their resolutions.
Torsion Part of ℤ-module
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].
Torsion Z-module and Torsion-free Z-module
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].
Torsion-free abelian groups and completely decomposable -adic modules