Taiwanese Journal of Mathematics

A Counterexample for a Problem on Quasi Baer Modules

Christian Lomp

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In this note we provide a counterexample to two questions on quasi-Baer modules raised recently by Lee and Rizvi in [5].

Article information

Taiwanese J. Math., Volume 21, Number 6 (2017), 1277-1281.

Received: 21 November 2016
Revised: 12 March 2017
Accepted: 12 March 2017
First available in Project Euclid: 17 August 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16D80: Other classes of modules and ideals [See also 16G50]
Secondary: 13C05: Structure, classification theorems 16D70: Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation 16W20: Automorphisms and endomorphisms

quasi-Baer modules quasi-retractable local-retractable


Lomp, Christian. A Counterexample for a Problem on Quasi Baer Modules. Taiwanese J. Math. 21 (2017), no. 6, 1277--1281. doi:10.11650/tjm/8028. https://projecteuclid.org/euclid.twjm/1502935248

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  • W. E. Clark, Twisted matrix units semigroup algebras, Duke Math. J. 34 (1967), no. 3, 417–423. https://doi.org/10.1215/s0012-7094-67-03446-1
  • M. Cohen and S. Montgomery, Group-graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), no. 1, 237–258. https://doi.org/10.2307/1999586
  • I. Kaplansky, Rings of Operators, W. A. Benjamin, New York-Amsterdam, 1968.
  • T. Y. Lam, A First Course in Noncommutative Rings, Second edition, Graduate Texts in Mathematics 131, Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4419-8616-0
  • G. Lee and S. Tariq Rizvi, Direct sums of quasi-Baer modules, J. Algebra 456 (2016), 76–92. https://doi.org/10.1016/j.jalgebra.2016.01.039
  • C. Lomp, A central closure construction for certain algebra extensions: Applications to Hopf actions, J. Pure Appl. Algebra 198 (2005), no. 1-3, 297–316. https://doi.org/10.1016/j.jpaa.2004.10.009
  • S. T. Rizvi and C. S. Roman, Baer and quasi-Baer modules, Comm. Algebra 32 (2004), no. 1, 103–123. https://doi.org/10.1081/agb-120027854
  • ––––, On direct sums of Baer modules, J. Algebra 321 (2009), no. 2, 682–696. https://doi.org/10.1016/j.jalgebra.2008.10.002