Endomorphisms and product bases of the Baer-Specker group.
Every Cotorsion-free Algebra is an Endomorphism Algebra.
Factor-splitting Abelian groups of arbitrary rank
Finite Groups of Exponent 12 as Automorphism Groups.
Free subgroups in the endomorphism ring of an Abelian free group
-nilpotent units of commutative group rings
Suppose is a commutative unital ring and is an abelian group. We give a general criterion only in terms of and when all normalized units in the commutative group ring are -nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].
Generalized Almost Completely Decomposable Groups
Generalized E-algebras via λ-calculus I
An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra of the R-module , taking any a ∈ A to the right multiplication by a, is an isomorphism of algebras. In this case is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18, 19]. Despite...
Generators of Free Product with Amalgamation of two Infinite Cyclic Groups.
Groupes -réduits
Gruppi monotóni di successioni intere
Homomorphisms between -projective Abelian groups and left Kasch-rings
Glaz and Wickless introduced the class of mixed abelian groups which have finite torsion-free rank and satisfy the following three properties: i) is finite for all primes , ii) is isomorphic to a pure subgroup of , and iii) is torsion. A ring is a left Kasch ring if every proper right ideal of has a non-zero left annihilator. We characterize the elements of such that is a left Kasch ring, and discuss related results.
Independence in Completions and Endomorphism Algebras.
Iterated countable products and sums of the infinite cyclic group
Large superdecomposable E(R)-algebras
For many domains R (including all Dedekind domains of characteristic 0 that are not fields or complete discrete valuation domains) we construct arbitrarily large superdecomposable R-algebras A that are at the same time E(R)-algebras. Here "superdecomposable" means that A admits no (directly) indecomposable R-algebra summands ≠ 0 and "E(R)-algebra" refers to the property that every R-endomorphism of the R-module, A is multiplication by an element of, A.
Locally free modules
Martin's Axiom Implies the Existence of Certain Slender Groups.
Measurable products of modules
Note on Direct Decompositions of Torsion-free Abelian Groups
Note on initial topologies on rational vector spaces induced by revalued linear mappings.