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Torsion Modules, Lattices and P-Points

Torsion Modules, Lattices and P-Points 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∈IAi ≠ 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. © London Mathematical Society http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Oxford University Press

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References (10)

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

Abstract

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∈IAi ≠ 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. © London Mathematical Society

Journal

Bulletin of the London Mathematical SocietyOxford University Press

Published: Sep 1, 1997

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