Tribak, RachidTutuncu, Derya KeskinErtas, Nil Orhan2024-09-292024-09-2920161405-213X2296-4495https://doi.org/10.1007/s40590-015-0068-4https://hdl.handle.net/20.500.14619/4290A module M is called ADS* if for every direct summand N of M and every supplement K of N in M, we have M = N circle plus K. In this work, we study direct sums of ADS* modules. Many examples are provided to show that this notion is not inherited by direct sums. It is shown that if a module M has a decomposition M = A circle plus B which complements direct summands such that A and B are mutually projective, then M is ADS*. The class of rings R, for which all direct sums of ADS* R-modules are ADS*, is shown to be exactly that of the right V-rings. We characterize the class of right perfect rings R for which R circle plus S is ADS* for every simple R-module S as that of the semisimple rings.eninfo:eu-repo/semantics/closedAccessSupplement submoduleADS* moduleV-ringArticle10.1007/s40590-015-0068-42-s2.0-85053692923461Q23322WOS:000371901300003N/A