Cotorsion theories cogenerated by N1-free abelian groups

Saharon Shelah; Lutz Strüngmann

doi:10.1216/rmjm/1181070044

Cotorsion theories cogenerated by N₁-free abelian groups

Saharon Shelah, Lutz Strüngmann

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Given an N₁-free abelian group G we characterize the class C_G of all torsion abelian groups T satisfying Ext (G, T) = 0 assuming the special continuum hypothesis C_H. Moreover, in Gödel’s constructible universe we prove that this characterizes C_G for arbitrary torsion-free abelian G. It follows that there exists some ugly N₁-free abelian groups.

Original language	English
Pages (from-to)	1617-1626
Number of pages	10
Journal	Rocky Mountain Journal of Mathematics
Volume	32
Issue number	4
DOIs	https://doi.org/10.1216/rmjm/1181070044
State	Published - 2002

Access to Document

10.1216/rmjm/1181070044

Cite this

@article{456afa24f87d40a29bff6ee390a13b5c,

title = "Cotorsion theories cogenerated by N1-free abelian groups",

abstract = "Given an N1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext (G, T) = 0 assuming the special continuum hypothesis CH. Moreover, in G{\"o}del{\textquoteright}s constructible universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exists some ugly N1-free abelian groups.",

author = "Saharon Shelah and Lutz Str{\"u}ngmann",

year = "2002",

doi = "10.1216/rmjm/1181070044",

language = "אנגלית",

volume = "32",

pages = "1617--1626",

journal = "Rocky Mountain Journal of Mathematics",

issn = "0035-7596",

publisher = "Rocky Mountain Mathematics Consortium",

number = "4",

}

TY - JOUR

T1 - Cotorsion theories cogenerated by N1-free abelian groups

AU - Shelah, Saharon

AU - Strüngmann, Lutz

PY - 2002

Y1 - 2002

N2 - Given an N1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext (G, T) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructible universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exists some ugly N1-free abelian groups.

AB - Given an N1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext (G, T) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructible universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exists some ugly N1-free abelian groups.

UR - https://www.scopus.com/pages/publications/0037570813

U2 - 10.1216/rmjm/1181070044

DO - 10.1216/rmjm/1181070044

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0037570813

SN - 0035-7596

VL - 32

SP - 1617

EP - 1626

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 4

ER -

Cotorsion theories cogenerated by N₁-free abelian groups

Abstract

Access to Document

Other files and links

Fingerprint

Cite this