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A counterexample for a problem on quasi Baer modules. (English) Zbl 1386.16002

Summary: In this note we provide a counterexample to two questions on quasi-Baer modules raised recently by [G. Lee and S. Tariq Rizvi, J. Algebra 456, 76–92 (2016; Zbl 1352.16008)].

MSC:

16D80 Other classes of modules and ideals in associative algebras
13C05 Structure, classification theorems for modules and ideals in commutative rings
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16W20 Automorphisms and endomorphisms

Citations:

Zbl 1352.16008
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References:

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[2] 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 · Zbl 0533.16001
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[5] 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 · Zbl 1352.16008
[6] 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 · Zbl 1084.16032
[7] 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 · Zbl 1072.16007
[8] —-, On direct sums of Baer modules, J. Algebra 321 (2009), no. 2, 682-696. https://doi.org/10.1016/j.jalgebra.2008.10.002 · Zbl 1217.16009
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