# Sh:716

• Göbel, R., & Shelah, S. (2001). Decompositions of reflexive modules. Arch. Math. (Basel), 76(3), 166–181.
• Abstract:
We continue [GbSh:568], proving a stronger result under the special continuum hypothesis (CH). The original question of Eklof and Mekler related to dual abelian groups. We want to find a particular example of a dual group, which will provide a negative answer to the question. In order to derive a stronger and also more general result we will concentrate on reflexive modules over countable principal ideal domains R. Following H. Bass, an R-module G is reflexive if the evaluation map \sigma:G\longrightarrow G^{**} is an isomorphism. Here G^*={\rm Hom} (G,R) denotes the dual group of G. Guided by classical results the question about the existence of a reflexive R-module G of infinite rank with G\not\cong G\oplus R is natural. We will use a theory of bilinear forms on free R-modules which strengthens our algebraic results in [GbSh:568]. Moreover we want to apply a model theoretic combinatorial theorem from [Sh:e] which allows us to avoid the weak diamond principle. This has the great advantage that the used prediction principle is still similar to the diamond, but holds under CH.
• Current version: 2000-02-19_11 (21p) published version (16p)
Bib entry
@article{Sh:716,
author = {G{\"o}bel, R{\"u}diger and Shelah, Saharon},
title = {{Decompositions of reflexive modules}},
journal = {Arch. Math. (Basel)},
fjournal = {Archiv der Mathematik},
volume = {76},
number = {3},
year = {2001},
pages = {166--181},
issn = {0003-889X},
mrnumber = {1816987},
mrclass = {20K20 (03E35 13C13 20K30)},
doi = {10.1007/s000130050557},
note = {\href{https://arxiv.org/abs/math/0003165}{arXiv: math/0003165}},
arxiv_number = {math/0003165}
}