Search

The main result of this paper gives several characterizations for Abelian groups A to have the property that the class of A-adstatic modules is closed with respect to submodules of bounded index. Especially, a group has this property if and only if it is flat and faithful with respect to torsion when viewed as a left module over its endomorphism ring. [ABSTRACT FROM AUTHOR]

An abelian group A is quotient divisible if its torsion subgroup tA is reduced, and it contains a finitely generated free subgroup F such that A/F is the direct sum of a finite and a divisible torsion group. This paper focuses on homological properties of quotient divisible groups. A group A such that tA is reduced is quotient divisible if and only if it is small with respect to the class of quotient divisible groups. Further results investigate when an A-generated torsion group is A-solvable. The last section discusses quotient divisible groups A such that ... ⊗z E(A)/tE(A) is a quasi-Frobenius ring. [ABSTRACT FROM AUTHOR]