A study on the $\pi$-dual Rickart modules

Document Type : Dedicated to Prof. O. A. S. Karamzadeh


Department of Mathematics, University of Hacettepe, P.O. Box 06800, Ankara, Turkey.


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.


Main Subjects

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