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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A solution to the Baer splitting problem


Authors: Lidia Angeleri Hügel, Silvana Bazzoni and Dolors Herbera
Journal: Trans. Amer. Math. Soc. 360 (2008), 2409-2421
MSC (2000): Primary 13C05, 16E30; Secondary 13G05, 16D40
Published electronically: December 11, 2007
MathSciNet review: 2373319
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Abstract: Let $ R$ be a commutative domain. We prove that an $ R$-module $ B$ is projective if and only if $ \mathrm{Ext}_R^1(B,T)=0$ for any torsion module $ T$. This answers in the affirmative a question raised by Kaplansky in 1962.


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Additional Information

Lidia Angeleri Hügel
Affiliation: Dipartimento di Informatica e Comunicazione, Università degli Studi dell’Insubria, Via Mazzini 5, I - 21100 Varese, Italy
Email: lidia.angeleri@uninsubria.it

Silvana Bazzoni
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, I-35121 Padova, Italy
Email: bazzoni@math.unipd.it

Dolors Herbera
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain
Email: dolors@mat.uab.es

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04255-9
PII: S 0002-9947(07)04255-9
Keywords: Baer modules, Mittag-Leffler inverse systems
Received by editor(s): October 26, 2005
Received by editor(s) in revised form: January 19, 2006
Published electronically: December 11, 2007
Additional Notes: The first and second authors were supported by Università di Padova (Progetto di Ateneo CDPA048343 “Decomposition and tilting theory in modules, derived and cluster categories”). The first and third authors were supported by the DGI and the European Regional Development Fund, jointly, through Project MTM2005-00934. The third author was supported by the Comissionat per Universitats i Recerca of the Generalitat de Catalunya and by the “Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni” (Italy). Part of this paper was written while the third author was visiting the universities in Padova and in Varese; she wants to thank her hosts for their hospitality
Article copyright: © Copyright 2007 American Mathematical Society