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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A solution to the Baer splitting problem
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by Lidia Angeleri Hügel, Silvana Bazzoni and Dolors Herbera PDF
Trans. Amer. Math. Soc. 360 (2008), 2409-2421 Request permission

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
  • MR Author ID: 358523
  • Email: lidia.angeleri@uninsubria.it
  • Silvana Bazzoni
  • Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, I-35121 Padova, Italy
  • MR Author ID: 33015
  • 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
  • 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
  • © Copyright 2007 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 2409-2421
  • MSC (2000): Primary 13C05, 16E30; Secondary 13G05, 16D40
  • DOI: https://doi.org/10.1090/S0002-9947-07-04255-9
  • MathSciNet review: 2373319