We investigate what 
${\rm Ext}(A,\mathbb{Z})$
 can be when A is torsion-free and 
${\rm Hom}(A,\mathbb{Z})=0$
 . We thereby give an answer to a question of Golasinski and Goncalves which asks for the divisible Abelian groups which can be the type of a co-Moore space.

Infinite Abelian groups

The structure of Ext(A, Z) and GCH: possible co-Moore spaces

Strongly homogeneous torsion-free Abelian groups

Similar to the idea of relative projectivity, we introduce the notion of relative subprojectivity, which is an alternative way to measure the projectivity of a module. Given modules $M$ and $N$, $M$ is said to be {\em $N$-subprojective} if for every epimorphism $g:B \rightarrow N$ and homomorphism $f:M \rightarrow N$, then there exists a homomorphism $h:M \rightarrow B$ such that $gh=f$. For a module $M$, the {\em subprojectivity domain of $M$} is defined to be the collection of all modules $N$ such that $M$ is $N$-subprojective. A module is projective if and only if its subprojectivity domain consists of all modules. Opposite to this idea, a module $M$ is said to be {\em subprojectively poor}, or {\em $sp$-poor} if its subprojectivity domain is as small as conceivably possible, that is, consisting of exactly the projective modules. Properties of subprojectivity domains and $sp$-poor modules are studied. In particular, the existence of an $sp$-poor module is attained for artinian serial rings.

/pdf/an-alternative-perspective-on-projectivity-of-modules-52gcbh14au.pdf

An alternative perspective on projectivity of modules

background

Quantum-corrected scattering and absorption of a Schwarzschild black hole with GUP

While it is known that the tensor product of two dimension groups is a dimension group, the corresponding problem for interpolation groups has been open for a while. We solve this problem here, by proving that the tensor product of two interpolation groups may not be an interpolation group, even for directed, torsion-free interpolation groups. We also solve the corresponding problems for refinement monoids (with tensor product of commutative monoids) and for lattice-ordered groups (with tensor product of partially ordered abelian groups).

https://msp.org/pjm/1996/176-1/pjm-v176-n1-p16-p.pdf

Infinite Abelian groups

Citations

The structure of Ext(A, Z) and GCH: possible co-Moore spaces

Strongly homogeneous torsion-free Abelian groups

An alternative perspective on projectivity of modules

Quantum-corrected scattering and absorption of a Schwarzschild black hole with GUP

Tensor products of structures with interpolation

Related Papers (5)

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