TY - JOUR
T1 - Baer modules over domains
AU - Eklof, Paul C.
AU - Fuchs, Laszlo
AU - Shelah, Saharon
PY - 1990/12
Y1 - 1990/12
N2 - 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.
AB - 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.
KW - Baer module
KW - Constructibility
KW - Continuous ascending chains
KW - Flat and projective modules
KW - Proper Forcing Axiom
KW - Prüfer domains
KW - Singular compactness
UR - http://www.scopus.com/inward/record.url?scp=0038448132&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1990-0974514-8
DO - 10.1090/S0002-9947-1990-0974514-8
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AN - SCOPUS:0038448132
SN - 0002-9947
VL - 322
SP - 547
EP - 560
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -