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Torsion Modules, Lattices and P‐Points

Torsion Modules, Lattices and P‐Points 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

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References (10)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S0024609397003329
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Sep 1, 1997

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