A characterization of Ext(G,ℤ) assuming (V = L)

• Autorzy: Saharon Shelah , Lutz Strüngmann
• Języki publikacji: EN

Abstrakty

EN

We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel's axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence $(ν_{p}: p ∈ Π)$ of cardinals satisfying $ν_{p} ≤ 2^{ν}$ (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that $ν_{p}$ equals the p-rank of Ext(G,ℤ) for every prime p and $2^{ν}$ is the torsion-free rank of Ext(G,ℤ).

Kategorie tematyczne

• 20K35: Extensions
• 20J05: Homological methods in group theory
• 20K40: Homological and categorical methods
• 20K20: Torsion-free groups, infinite rank
• 18E99: None of the above, but in this section
• 20K15: Torsion-free groups, finite rank

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 193
• Numer: 2
• Strony: 141-151

Daty

wydano

2007

Twórcy

autor

Saharon Shelah

• Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
• Rutgers University, New Brunswick, NJ 08903, U.S.A.

autor

Lutz Strüngmann

• Department of Mathematics, University of Duisburg-Essen, 45117 Essen, Germany
• Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, HI 96822-2273, U.S.A.

Identyfikatory

DOI

10.4064/fm193-2-3