Abstract
A QTAG-module M is an alpha-module, where alpha is a limit ordinal, if M/H-beta(M) is totally projective for every ordinal beta < alpha. Here we show that totally projective modules and alpha-modules of length alpha, where alpha has cofinality omega, are projectively socle-regular. We also show that a summable omega(1)-module need not be a direct sum of countably generated modules, where omega(1) is the first uncountable ordinal.