  Henselian elements are roots of polynomials which satisfy the conditions of
Hensel's Lemma. In this paper we prove that for a finite field extension
$(F|L,v)$, if $F$ is contained in the absolute inertia field of $L$, then the
valuation ring $\mathcal O_F$ of $(F,v)$ is generated as an $\mathcal
O_L$-algebra by henselian elements. Moreover, we give a list of equivalent
conditions under which $\mathcal O_F$ is generated over $\mathcal O_L$ by
finitely many henselian elements. We prove that if the chain of prime ideals of
$\mathcal O_L$ is well-ordered, then these conditions are satisfied. We give an
example of a finite valued inertial extension $(F|L,v)$ for which $\mathcal
O_F$ is not a finitely generated $\mathcal O_L$-algebra. We also present a
theorem that relates the problem of local uniformization with the theory of
henselian elements.
