Baer modules over domains

Paul C. Eklof; Laszlo Fuchs; Saharon Shelah

doi:10.1090/S0002-9947-1990-0974514-8

Baer modules over domains

Paul C. Eklof
, Laszlo Fuchs
, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

Abstract

For a commutative domain R with 1, an R-module B is called a Baer module if for all torsion K-modules T. The structure of Baer modules over arbitrary domains is investigated, and the problem is reduced to the case of countably generated Baer modules. This requires a general version of the singular compactness theorem. As an application we show that over hlocal Prüfer domains, Baer modules are necessarily projective. In addition, we establish an independence result for a weaker version of Baer modules.

Original language	English
Pages (from-to)	547-560
Number of pages	14
Journal	Transactions of the American Mathematical Society
Volume	322
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1990-0974514-8
State	Published - Dec 1990

Keywords

Baer module
Constructibility
Continuous ascending chains
Flat and projective modules
Proper Forcing Axiom
Prüfer domains
Singular compactness

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10.1090/S0002-9947-1990-0974514-8

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abstract = "For a commutative domain R with 1, an R-module B is called a Baer module if for all torsion K-modules T. The structure of Baer modules over arbitrary domains is investigated, and the problem is reduced to the case of countably generated Baer modules. This requires a general version of the singular compactness theorem. As an application we show that over hlocal Pr{\"u}fer domains, Baer modules are necessarily projective. In addition, we establish an independence result for a weaker version of Baer modules.",

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KW - Constructibility

KW - Continuous ascending chains

KW - Flat and projective modules

KW - Proper Forcing Axiom

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KW - Singular compactness

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Baer modules over domains

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Keywords

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