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G. Bergman, F. Galvin (1987)
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Answering a long‐standing question in the theory of torsion modules, we show that weakly productively bounded domains are necessarily productively bounded. (See the Introduction for definitions.) Moreover, we prove a twin result for the ideal lattice L of a domain equating weak and strong global intersection conditions for families (Xi)i∈I of subsets of L with the property that ∩i∈I Ai ≠ 0 whenever Ai∈Xi. Finally, we show that for domains with Krull dimension (and countably generated extensions thereof), these lattice‐theoretic conditions are equivalent to productive boundedness. 1991 Mathematics Subject Classification 03E05, 06A23, 13C12, 16U20, 16P60.
Bulletin of the London Mathematical Society – Wiley
Published: Sep 1, 1997
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