  The ordinariness of elliptic curves is essential in proving various expected
properties of elliptic curves in positive characteristic and can be extended to
algebraic curves of arbitrary genus. The present paper deals with another kind
of extension, i.e., ordinariness of dormant $\mathfrak{sl}_2$-opers, or more
generally, dormant $\mathfrak{sl}_n$-opers. We prove that, for dormant
$\mathfrak{sl}_2$-opers on elliptic curves, this notion is essentially
equivalent to the classical ordinariness. Moreover, the main result of the
present paper asserts that the pull-back of an ordinary dormant
$\mathfrak{sl}_n$-oper on a general curve by a cyclic covering is ordinary
whenever the order of its Galois group is prime to the characteristic of the
base field. This result may be regarded as an analogue of a result by S.
Nakajima for ordinary algebraic curves.
