On α-Modules and Their Applications.

A QTAG-module M is an α-module, where α is a limit ordinal, if M/Hβ(M) is totally projective for every ordinal β < α. Here we show that totally projective mod- ules and α-modules of length α, where α has cofinality ω, are projectively socle-regular. We also show that a summable ω1-module need not be a direct sum of countably gen- erated modules, where ω1 is the first uncountable ordinal. [ABSTRACT FROM AUTHOR]