Transactions of the American Mathematical Society

Author(s): Lidia Angeleri Hügel; Silvana Bazzoni; Dolors Herbera
Journal: Trans. Amer. Math. Soc. 360 (2008), 2409-2421.
MSC (2000): Primary 13C05, 16E30; Secondary 13G05, 16D40
Posted: December 11, 2007
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Abstract: Let

be a commutative domain. We prove that an

-module

is projective if and only if $\mathrm{Ext}_R^1(B,T)=0$ for any torsion module

. This answers in the affirmative a question raised by Kaplansky in 1962.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 13C05, 16E30, 13G05, 16D40

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: 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
Posted: 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
Copyright of article: Copyright 2007, American Mathematical Society

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