%0 Journal Article
%T A note on ADS* modules
%A Derya Keskin T¨¹t¨¹nc¨¹
%J Bulletin of Mathematical Sciences
%@ 1664-3615
%D 2012
%I Springer
%R 10.1007/s13373-012-0020-0
%X We study the ADS* modules which are the dualizations of ADS modules studied by Alahmadi et al. (J Algebra 352:215¨C222, 2012). Mainly we prove that an amply supplemented module M is ADS* if and only if M 1 and M 2 are mutually projective whenever ${M = M_{1} \oplus M_{2}}$ if and only if for any direct summand S 1 and a submodule S 2 with M = S 1 + S 2, the epimorphism ${\alpha_{i} : M \longrightarrow S_{i}/(S_{1} \cap S_{2})}$ with Ker (¦Á i ) = S j (i ¡Ù j = 1, 2) can be lifted to an idempotent endomorphism ¦Â i of M with ${\beta_{i}(M) \subseteq S_{i}}$ .
%K Supplement submodule
%K Amply supplemented module
%K ¦Ð-Projective modules
%K ADS* module
%K 16D20
%K 16D80
%U http://link.springer.com/article/10.1007/s13373-012-0020-0