The structure of an almost artinian module.
The structure of indecomposable injective modules.
The theta ideal, dense submodules and the forcing linearity number for a multiplication module.
The torsion theory and the Melkersson condition
We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring. In 2008 Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition in local cohomology theory. One of our purposes in this paper is to show how naturally the concept of Melkersson condition...
The total graph of a module
Tight closure of parameter ideals.
Torsion äußerer Potenzen von Moduln der homologischen Dimension l.
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
Torsion-free modules and syzygies.
Trace Ideals of Relation Modules of Finite Groups.
Two applications of dualizing complexes over local rings
Two Notes on Flatness.
Two properties of the power series ring.
Two versions of Nakayama lemma for multiplication modules.
Typical sheaves of generalized CM-Modules.
Über Automorphismen eines Annullatorenverbandes gewisser Teilringe im Endomorphismenring eines homogenen vollständig reduziblen Moduls
Über das Verhalten der Betti-Reihe eines lokalen Ringes bei monoidalen Transformationen
Über den regulären Ort in ausgezeichneten Ringen.