Number of indecomposable summands in direct decompositions of torsion-free abelian groups
On a class of locally Butler groups
A torsionfree abelian group is called a Butler group if for any torsion group . It has been shown in [DHR] that under any countable pure subgroup of a Butler group of cardinality not exceeding is again Butler. The purpose of this note is to show that this property has any Butler group which can be expressed as a smooth union of pure subgroups having countable typesets.
On a class of locally completely decomposable Abelian groups
On a class of torsionfree Abelian groups [Abstract of thesis]
On a generalization of a Prüfer-Kaplansky-Procházka theorem
On abelian groups by which balanced extensions of a rational group split. II
On Cartesian Powers of a Rational Group.
On chains of free modules over valuation domains
On decomposable fully transitive torsion-free groups.
On Direct Summands of A-Separable R-Modules.
On Fuchs' problem 76.
On reduced products of abelian groups
On some subgroups of infinite rank Butler groups
On summands of direct products of Abelian groups
On the Rank of Ext.
Prescribing endomorphism algebras of -free modules
It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case the authors...
Pure subgroups
Let be an infinite cardinal. Set , define for every , take as the first cardinal with , and put . If is a torsion-free group of cardinality at least and is its subgroup such that is torsion and , then contains a non-zero subgroup pure in . This generalizes the result from a previous paper dealing with -primary.
Pure subgroups split
Quasi-Direct Decompositions of Torsion-Free Abelian Groups of Infinite Rank.
Rings on certain classes of torsion-free Abelian groups