Infinite Abelian groups

Classifying E-Rings

The Fine Structure of the Kasparov Groups II: Topologizing the UCT

We analyze the complexity of the bi-embeddability relations for countable torsion-free abelian groups and for countable torsion abelian groups.

The bi-embeddability relation for countable abelian groups

/pdf/a-note-on-locally-a-projective-groups-3pyfe3ae3t.pdf

A note on locally $A$-projective groups.

We describe inertial endomorphisms of an abelian group $A$, that is endomorphisms $\varphi $ with the property $|(\varphi (X)+X)/X|<\infty $ for each $X\le A$. They form a ring $IE(A)$ containing the ideal $F(A)$ formed by the so-called finitary endomorphisms, the ring of power endomorphisms and also other non-trivial instances. We show that the quotient ring $IE(A)/F(A)$ is commutative. Moreover, inertial invertible endomorphisms form a group, provided $A$ has finite torsion-free rank. In any case, the group $IAut(A)$ they generate is commutative modulo the group $FAut(A)$ of finitary automorphisms, which is known to be locally finite. We deduce that $IAut(A)$ is locally-(center-by-finite). Also, we consider the lattice dual property, that is $|X/(X\cap \varphi (X))|<\infty $ for each $X\le A$ and show that this implies the above one, provided $A$ has finite torsion-free rank.

methods

/pdf/inertial-endomorphisms-of-an-abelian-group-2owf7z02qm.pdf

Infinite Abelian groups

Citations

Classifying E-Rings

The Fine Structure of the Kasparov Groups II: Topologizing the UCT

The bi-embeddability relation for countable abelian groups

A note on locally $A$-projective groups.

Inertial endomorphisms of an abelian group

Related Papers (5)

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