A note on clean abelian groups
A note on coflat abelian groups
A theorem on groups
Abelian group pairs having a trivial coGalois group
Torsion-free covers are considered for objects in the category Objects in the category are just maps in -Mod. For we find necessary and sufficient conditions for the coGalois group associated to a torsion-free cover, to be trivial for an object in Our results generalize those of E. Enochs and J. Rado for abelian groups.
Abelian groups of zero adjoint entropy
The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of zero adjoint...
Abelian groups which have trivial absolute coGalois group
In this article we characterize those abelian groups for which the coGalois group (associated to a torsion free cover) is equal to the identity.
Abelian groups whose endomorphism ring is linearly compact
Abelian Groups with an Endomorphism with Irreducible minimum Polynomial
Abelian groups with anti-isomorphic endomorphism rings
Abelian groups with many automorphisms
AE-rings
Algebras determined by their endomorphism monoids
An extension of Zassenhaus' theorem on endomorphism rings
Let R be a ring with identity such that R⁺, the additive group of R, is torsion-free. If there is some R-module M such that and , we call R a Zassenhaus ring. Hans Zassenhaus showed in 1967 that whenever R⁺ is free of finite rank, then R is a Zassenhaus ring. We will show that if R⁺ is free of countable rank and each element of R is algebraic over ℚ, then R is a Zassenhaus ring. We will give an example showing that this restriction on R is needed. Moreover, we will show that a ring due to A....
A-Rings
A ring R is called an E-ring if every endomorphism of R⁺, the additive group of R, is multiplication on the left by an element of R. This is a well known notion in the theory of abelian groups. We want to change the "E" as in endomorphisms to an "A" as in automorphisms: We define a ring to be an A-ring if every automorphism of R⁺ is multiplication on the left by some element of R. We show that many torsion-free finite rank (tffr) A-rings are actually E-rings. While we have an example of a mixed...
Automorphisms of abelian -groups and hypo residual finiteness
Automorphisms of Bounded Abelian Groups.