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].
Eine Bemerkung zur Theorie der ...-Ringe.
Endomorphism algebras over large domains
The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain
Essentially indecomposable modules over a complete discrete valuation ring
Every Cotorsion-free Algebra is an Endomorphism Algebra.
Exact sequences of pairs in commutative rings
Extensionless modules over tame hereditary algebras
Failure of splitting from module-finite extension rings.
Finite and infinite collections of multiplication modules.
Finitely generated projective ideals in commutative rings.
Finitely generated projective modules and Fitting ideals.
Fittings's Invariants and a Theorem of Grauert.
Fully inert submodules of torsion-free modules over the ring of p-adic integers
Fully inert submodules of torsion-free -modules are investigated. It is proved that if the module considered is either free or complete, these submodules are exactly those which are commensurable with fully invariant submodules; examples are given of torsion-free -modules for which this property fails.
Functorial Subgroups Commuting with Inverse Limits.
Generating ideals in local rings using elements of high degrees.
Generators for Certain Ideals in Regular Rings of Dimension Three
Generic maps and modules
Hereditary tensor-orthogonal theories
Independence in Completions and Endomorphism Algebras.