Pseudo-partitives are strings of the form [N1 – of – N2] in which N1 denotes a quantity or amount of whatever it is that N2 denotes and in which N2 is a bare nominal. Such strings come in two types, depending on whether the combination shares the number value of N1 or N2. The first type can be analyzed along familiar lines, but the second one is a hard nut to crack. The article presents existing treatments, showing that they all involve departures from independently motivated principles. As an alternative we propose an analysis that is cast in the Typed Feature Structure notation of Head-driven Phrase Structure Grammar. It handles both types of pseudo-partitives, arguing that N1 and the preposition of are complement-selecting heads if the number value is shared with N1, while N1 and the preposition are head-selecting functors if the number value is shared with N2. The switch from head to functor status is characteristic of grammaticalization and is shown to affect pseudo-partitives with a quantifier noun or a collection noun as N1, but not pseudo-partitives with a measure noun or collection noun. Examples and quantitative data are extracted from COCA.

In this paper, we characterize quadratic number fields possessing unique factorization in terms of the power cancellation property of torsion-free rank-two abelian groups, in terms of Σ-unique decomposition, in terms of a pair of point set topological properties of Eilenberg–Mac Lane spaces, and in terms of the sequence of rational primes. We give a complete set of topological invariants of abelian groups, we characterize those abelian groups that have the power cancellation property in the category of abelian groups, and we characterize those abelian groups that have Σ-unique decomposition. Our methods can be used to characterize any direct sum decomposition property of an abelian group.