%0 Journal Article
%T A study on the $\pi$-dual Rickart modules
%J Journal of the Iranian Mathematical Society
%I Iranian Mathematical Society
%Z 2717-1612
%A Keskin Tütüncü, D.
%D 2023
%\ 07/01/2023
%V 4
%N 2
%P 235-245
%! A study on the $\pi$-dual Rickart modules
%K dual Baer module
%K $\pi$-dual Baer module
%K dual Rickart module
%K $\pi$-dual Rickart module
%K projection invariant submodule
%R 10.30504/jims.2023.396908.1114
%X The 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.
%U https://jims.ims.ir/article_176734_8c062dd1c99f98165c4c961539c21b50.pdf