Infinitary Equivalence of Zp- Modules with Nice Decomposition Bases

Authors

Rüdiger Göbel, Universitat Duisburg-Essen, Germany 
Katrin Leistner, Universitat Duisburg-Essen, GermanyFollow
Peter Loth, Sacred Heart UniversityFollow
Lutz Strüngmann, Universitat Duisburg-Essen, Germany

Document Type

Article

Publication Date

Fall 2011

Abstract

Warfield modules are direct summands of simply presented Z_p - modules, or, alternatively, are Z_p - modules possessing a nice decomposition basis with simply presented cokernel. They have been classified up to isomorphism by theor Ilm-Kaplansky and Warfield invariants. Taking a model theoretic point of view and using infinitary languages we give here a complete theoretic characterization of a large class of Z_p - modules having a nice decomposition basis. As a corollary, we obtain the classical classification of countable Warfield modules. This generalizes results by Barwise and Eklof.

Comments

Originally published:

R. Göbel, K. Leistner, P. Loth and L. Strüngmann. "Infinitary equivalence of Z_p -modules with nice decomposition bases." Journal of Commutative Algebra 3.3 (Fall 2011): 321-348.

doi:10.1216/JCA-2011-3-3-321

Recommended Citation

Göbel, Rüdiger; Leistner, Katrin; Loth, Peter; and Strüngmann, Lutz, "Infinitary Equivalence of Zp- Modules with Nice Decomposition Bases" (2011). Mathematics Faculty Publications. 16.
https://digitalcommons.sacredheart.edu/math_fac/16