Dimensionstheorie in globalen Moduln.
Direct Sums of Dual Continuous Modules.
Discriminants of etale algebras and related structures.
Distributive homomorphisms of rings and modules.
Divisible ℤ-modules
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].
Divisorial cohomology vanishing on toric varieties.
Dualitätstheorie in den Moduln über einem Dedekindschen Ring