As noted in Section 2.1, Fqm may be viewed as a vector space of dimension m over Fq, and therefore has a basis (in fact, many bases) over Fq. Some fundamental definitions and results on bases were already given there. In particular, Theorem 2.1.93 and Corollary 2.1.95 provide criteria when a set {α1, . . . , αm} of elements in Fqm forms a basis over Fq.