## Rocky Mountain Journal of Mathematics

### The classification of infinite abelian groups with partial decomposition bases in $L_\infty \omega$

#### Abstract

We consider the class of abelian groups with partial decomposition bases, which includes groups classified by Ulm, Warfield, Stanton and others. We define an invariant and classify these groups in the language $L_{\infty \omega }$, or equivalently, up to partial isomorphism. This generalizes a result of Barwise and Eklof and builds on Jacoby's classification of local groups with partial decomposition bases in $L_{\infty \omega }$.

#### Article information

Source
Rocky Mountain J. Math., Volume 47, Number 2 (2017), 463-477.

Dates
First available in Project Euclid: 18 April 2017

https://projecteuclid.org/euclid.rmjm/1492502546

Digital Object Identifier
doi:10.1216/RMJ-2017-47-2-463

Mathematical Reviews number (MathSciNet)
MR3635370

Zentralblatt MATH identifier
06715757

#### Citation

Jacoby, Carol; Loth, Peter. The classification of infinite abelian groups with partial decomposition bases in $L_\infty \omega$. Rocky Mountain J. Math. 47 (2017), no. 2, 463--477. doi:10.1216/RMJ-2017-47-2-463. https://projecteuclid.org/euclid.rmjm/1492502546

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