Abstract
We study the ADS* modules which are the dualizations of ADS modules studied by Alahmadi et al. (J Algebra 352:215–222, 2012). Mainly we prove that an amply supplemented module M is ADS* if and only if M1 and M2 are mutually projective whenever \({M = M_{1} \oplus M_{2}}\) if and only if for any direct summand S1 and a submodule S2 with M = S1 + S2, the epimorphism \({\alpha_{i} : M \longrightarrow S_{i}/(S_{1} \cap S_{2})}\) with Ker (α i ) = S j (i ≠ j = 1, 2) can be lifted to an idempotent endomorphism β i of M with \({\beta_{i}(M) \subseteq S_{i}}\) .
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The author sincerely thank the referee for his/her numerous valuable comments in the report, which have largely improved the presentation of the paper.
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Communicated by S.K. Jain.
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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Keskin Tütüncü, D. A note on ADS* modules. Bull. Math. Sci. 2, 359–363 (2012). https://doi.org/10.1007/s13373-012-0020-0
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DOI: https://doi.org/10.1007/s13373-012-0020-0