Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16124220230701A study on the $\pi$-dual Rickart modules23524517673410.30504/jims.2023.396908.1114END.Keskin TütüncüDepartment of Mathematics, University
of Hacettepe, P.O. Box 06800, Ankara, Turkey.Journal Article20230511The right $R$-module $M$ is said to be a $\pi$-dual Rickart module, if for every endomorphism $f:M\to M$ with projection invariant image, $f(M)$, in $M$, $f(M)$ is a direct summand of $M$. We show that the class of the $\pi$-dual Rickart modules contains properly the class of all $\pi$-dual Baer modules and the dual Rickart modules. We also investigate the transfering between a base ring $R$ and $R[x]$ (and $R[[x]]$). It is shown that, in general, the class of $\pi$-dual Rickart modules is neither closed under direct summands nor closed under direct sums. We conclude the paper by giving a connection between the classes of $\pi$-dual Baer and $\pi$-lifting modules.https://jims.ims.ir/article_176734_8c062dd1c99f98165c4c961539c21b50.pdf