statement of the problem: implant-retained overdenture can improve the stability of dentures and prevent bone loss. overdenture-wearing patients need special hygiene care. purpose: the aim of this study was to evaluate the effects of various denture cleansers on the retention of dio orange o-rings. method and materials : in this experimental study, 40 dio orange o-rings were divided into 4 grou...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...