  The notion of normal elements for finite fields extension has been
generalized as k-normal elements by Huczynska et al. [3]. The number of
k-normal elements for a fixed finite field extension has been calculated and
estimated [3], and several methods to construct k-normal elements have been
presented [1,3]. Several criteria on k-normal element have been given [1,2]. In
this paper we present a new criterion on k-normal elements by using idempotents
and show some examples. Such criterion has been given for usual normal element
before [6].
