### Torsion modules, lattices and $p$-points

by Eklof and Huisgen-Zimmermann and Shelah. [EHSh:617]

Bulletin London Math Soc, 1997

Answering a long-standing question in the theory of torsion
modules, we show that weakly productively bounded domains are
necessarily productively bounded. Moreover, we prove a twin result
for the ideal lattice L of a domain equating weak and strong
global intersection conditions for families (X_i)_{i in I} of
subsets of L with the property that bigcap_{i in I} A_i ne 0
whenever A_i in X_i . Finally, we show that, for domains with Krull
dimension (and countably generated extensions thereof), these
lattice-theoretic conditions are equivalent to productive
boundedness.

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