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TORSION MODULES, LATTICES AND P-POINTS

Published online by Cambridge University Press:  01 September 1997

PAUL C. EKLOF ,
BIRGE HUISGEN-ZIMMERMANN  and
SAHARON SHELAH
PAUL C. EKLOF
Affiliation:
Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA
BIRGE HUISGEN-ZIMMERMANN
Affiliation:
Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
SAHARON SHELAH
Affiliation:
Mathematics Institute, Hebrew University, Jerusalem 91904, Israel
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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∈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.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 5 , September 1997 , pp. 547 - 555
Copyright
© The London Mathematical Society 1997

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