The Torsion-free Rank of Ext1(A,Z) and Whitehead’s Problem
Morena Porzio – GJM, Volume 7, Issue 1 (2022), 10-16.
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- septembre 10, 2022
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The aim of this article is to give an alternative proof of the characterization of the torsion-free rank of Ext^1(A,\mathbb{Z}) for countable torsion-free abelian groups A with torsion-free rank equals to 1, without using Stein’s Theorem. This leads to the characterization of the torsion-free rank of Ext ^1(A,\mathbb{Z}) given in Eklof and Mekler’s book Almost Free Modules. As a result, Whitehead’s conjecture is verified for the case of countable groups.
Milestones:
Received: July 03, 2019
Accepted: January 20, 2020
Revised: January 10, 2022
Published online: September 05, 2022
Authors:
Morena Porzio2990 Broadway,
Columbia University,
New York NY 10027, USA.