The characterization of (A) CR-groups studied by Shalom Feigelstock ['Additive groups of
commutative rings', Quaest. Math. 23 (2000), 241–245] is complemented. In particular, the …

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 relation between the structure of a ring and the structure of its additive group is studied
in the context of some recent results in additive groups of mixed rings. Namely, the notion of …

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 …

A TORSION-FREE ABELIAN GROUP EXISTS WHOSE QUOTIENT GROUP MODULO THE
SQUARE SUBGROUP IS NOT A NIL-GROUP Page 1 Bull. Aust. Math. Soc. 94 (2016), 449–456 …

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 …

The square subgroup of an abelian group (A,+, 0) which is denoted by□⁢ A, can be
understood as a subgroup of A generated by the squares of all possible rings defined on A …

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 …