Let $R$ be a commutative ring with identity and $a\in R$ has the property that for $b\in R$ if $\langle a\rangle\cap\langle b\rangle=\{0\}$, then $ann_R(a)+ann_R(b)=R$, where $ann_R(x) :=\{r\in R\mid rx=0 \}$ for $x\in R$. Is there any characterization for such an element?
Removed the deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)
Martin Sleziak
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