 To prove that every finite skew-field is a field, we use strong induction on the size of the skew-field.Thus, let "A" be a skew-field, and assume that all skew-fields that are proper subsets of "A" are fields.Since the center "Z"("A") of "A" is a field, "A" is a vector space over "Z"("A") with finite dimension "n".