  Let $(R, \mathfrak m)$ be a one dimensional local Cohen-Macaulay ring. An
$\mathfrak m$-primary ideal $I$ of $R$ is Elias if the types of $I$ and of
$R/I$ are equal. Canonical and principal ideals are Elias, and Elias ideals are
closed under inclusion. We give multiple characterizations of Elias ideals and
concrete criteria to identify them. We connect Elias ideals to other
well-studied definitions: Ulrich, $\mathfrak m$-full, integrally closed, trace
ideals, etc. Applications are given regarding canonical ideals, conductors and
the Auslander index.
