Globale und lokale Erzeugendenanzahl im Reellen.
Invariante Untermoduln quadratischer Moduln.
Lattice of ℤ-module
In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9]....
Local Chern classes, multiplicities, and perfect complexes
Matricial decomposition of systems over rings.
Modules for which the natural map of the maximal spectrum is surjective
Let R be a commutative ring with identity. The purpose of this paper is to introduce two new classes of modules over R, called Ms modules and fulmaximal modules respectively. The first (resp. second) class contains the family of finitely generated and primeful (resp. finitely generated and multiplication) modules properly. Our concern is to extend some properties of primeful and multiplication modules to these new classes of modules.
Notes on radical filters of ideals
On endomorphisms of multiplication and comultiplication modules
Let be a ring with an identity (not necessarily commutative) and let be a left -module. This paper deals with multiplication and comultiplication left -modules having right -module structures.
On extensions of partial -operators
On finitely generated multiplication modules
We shall prove that if is a finitely generated multiplication module and is a finitely generated ideal of , then there exists a distributive lattice such that with Zariski topology is homeomorphic to to Stone topology. Finally we shall give a characterization of finitely generated multiplication -modules such that is a finitely generated ideal of .
On prime submodules and primary decomposition
We characterize prime submodules of for a principal ideal domain and investigate the primary decomposition of any submodule into primary submodules of
On Rank 4 Quadratic Spaces with Given Arf and Witt Invariants.
On ring theoretic lattice modules
On the ring of the variety of algebras over a ring
On torsion free distributive modules.
Prime and primary submodules of certain modules
In this paper we characterize all prime and primary submodules of the free -module for a principal ideal domain and find the minimal primary decomposition of any submodule of . In the case , we also determine the height of prime submodules.
Rings Whose Modules Have Nice Decompositions.
Some results on homotopy theory of modules
Seguendo le idee presentate nei lavori [1] e [2] si studiano le proprietà dei gruppi di -omotopia per moduli ed omomorfismi di moduli.
Stability of algebraic inverse systems, I: Stability, weak stability and the weakly-stable socle
Star-invertible ideals of integral domains
Let be a star-operation on and the finite character star-operation induced by . The purpose of this paper is to study when or . In particular, we prove that if every prime ideal of is -invertible, then , and that if is a unique -factorable domain, then is a Krull domain.