let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.

Yoshizawa investigated when local cohomology modules have an annihilator that does not depend on the choice of defining ideal. In this paper we refine his results and investigate relationship between annihilators restricted flat dimensions.