The quasi-Baer-splitting property for mixed abelian groups

The R ∞ Property for Abelian Groups

It is well known there is no finitely generated abelian group which has the R∞ property. We will show that also many non-finitely generated abelian groups do not have the R∞ property, but this does not hold for all of them! In fact we construct an uncountable number of infinite countable abelian groups which do have the R∞ property. We also construct an abelian group such that the cardinality o...

non-divisibility for abelian groups

Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting   all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...

certain finite abelian groups with the redei $k$-property

‎three infinite families of finite abelian groups will be‎ ‎described such that each member of these families has‎ ‎the r'edei $k$-property for many non-trivial values of $k$‎.

Extensions of Baer and quasi-Baer modules

On quasi-baer modules

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.