In the class of torsion-free abelian groups of finite rank, Feigelstock's conjecture on the
equivalence of the notions of nil and associative nil groups is reduced to indecomposable …

The paper deals with new specific constructions of indecomposable torsion-free abelian
groups of rank two and nonzero rings on them. They illustrate purely theoretical results and …

A multiplication on an Abelian group G is a homomorphism μ: G⊗ G→ G. The set Mult G of
all multiplications on an Abelian group G itself is an Abelian group with respect to addition; …

The paper contains a simple solution of Stratton and Webb's problem related to the so-called
absolute annihilators of abelian groups researched also by Feigelstock. Namely, there are …

An abelian group A is called a TI-group if every associative ring with the additive group A is
filial. The filiality of a ring R means that the ring R is associative and all ideals of any ideal of …

It is studied how rank two pure subgroups of a torsion-free Abelian group of rank three
influences its structure and type set. In particular, the criterion for such a subgroup B to be a …

This paper deals with additive groups of rings in which all subrings are ideals. It is shown
that if an abelian group supports only rings with this property, then all of them are …

A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to
some questions posed in the mentioned paper are also given. The square subgroup of a …

For an Abelian group G, any homomorphism μ: G⊗ G→ G is called a multiplication on G. The
set Mult G of all multiplications on an Abelian group G itself is an Abelian group with respect …

The first example of a finite rank torsion-free abelian group A such that the quotient group of
A modulo the square subgroup of A is not a nil-group is indicated (in both cases of …