The Characteristic Subgroups of the Baer-Specker Group.
Very Decomposable Abelian Groups.
Essentially Rigid Floppy Subgroups of the Baer-Specker Group.
Die Struktur kartesischer Produkte ganzer Zahlen modulo kartesische Produkte ganzer Zahlen.
Martin's Axiom Implies the Existence of Certain Slender Groups.
Every Cotorsion-free Algebra is an Endomorphism Algebra.
Modules Over Arbitrary Domains.
Automorphism Groups of Fields.
On Endomorphism Rings of Primary Abelian Groups.
Independence in Completions and Endomorphism Algebras.
Algebraisch kompakte Faktorgruppen.
Prescribing endomorphism algebras. The cotorsion-free case
Testing for Cotorsionness over Domains
Embeddings of Kronecker modules into the category of prinjective modules and the endomorphism ring problem
Almost free splitters
Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which are larger...
Quotients of reflexive modules
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
Subgroups of the Baer–Specker group with few endomorphisms but large dual
Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to ℤ.
Modules over arbitrary domains II
Algebraic ramifications of the common extension problem for group-valued measures
Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.
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