On infinite Goldie dimension (Q1270388)

The paper presents a unified proof of the following two results: 1. If \(P\) is a partially ordered set and \(\delta(P)\) is the supremum of cardinals \(\kappa\) such that \(P\) contains a subset of pairwise disjoint elements with cardinal number \(\kappa\), then unless \(\delta(P)\) is weakly inaccessible, \(P\) contains a subset of pairwise disjoint elements with cardinal number \(\delta(P)\) (P. Erdős and A. Tarski). 2. Let \(Gd(M)\) denote the Goldie dimension of the module \(M\). Then, unless \(Gd(M)\) is weakly inaccessible, \(M\) contains a direct sum of \(Gd(M)\) submodules (J. Dauns and L. Fuchs).