The Classification of Zp -modules with Partial Decomposition Bases in L∞ω

Authors

Carol Jacoby
Peter Loth, Sacred Heart UniversityFollow

Document Type

Peer-Reviewed Article

Publication Date

11-2016

Abstract

Ulm’s Theorem presents invariants that classify countable abelian torsion groups up to isomorphism. Barwise and Eklof extended this result to the classification of arbitrary abelian torsion groups up to L∞ω-equivalence. In this paper, we extend this classification to a class of mixed Zp-modules which includes all Warfield modules and is closed under L∞ω-equivalence. The defining property of these modules is the existence of what we call a partial decomposition basis, a generalization of the concept of decomposition basis. We prove a complete classification theorem in L∞ω using invariants deduced from the classical Ulm and Warfield invariants.

Comments

Version posted in an arxiv.org preprint https://arxiv.org/pdf/1507.06572.pdf

DOI

10.1007/s00153-016-0506-7

Recommended Citation

Jacoby, C. & Loth, P. (2016). The classification of Zp-modules with partial decomposition basis in L∞ω. Archive for Mathematical Logic, 55(7), 939-954. doi:10.1007/s00153-016-0506-7