TY - JOUR
ID - 176734
TI - A study on the $\pi$-dual Rickart modules
JO - Journal of the Iranian Mathematical Society
JA - JIMS
LA - en
SN -
AU - Keskin Tütüncü, D.
AD - Department of Mathematics, University
of Hacettepe, P.O. Box 06800, Ankara, Turkey.
Y1 - 2023
PY - 2023
VL - 4
IS - 2
SP - 235
EP - 245
KW - dual Baer module
KW - $\pi$-dual Baer module
KW - dual Rickart module
KW - $\pi$-dual Rickart module
KW - projection invariant submodule
DO - 10.30504/jims.2023.396908.1114
N2 - 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.
UR - https://jims.ims.ir/article_176734.html
L1 - https://jims.ims.ir/article_176734_8c062dd1c99f98165c4c961539c21b50.pdf
ER -