  We study a canonical spanning surface obtained from a knot or link diagram
depending on a given Kauffman state, and give a sufficient condition for the
surface to be essential. By using the essential surface, we can see the
triviality and splittability of a knot or link from its diagrams. This has been
done on the extended knot or link class which includes all of semiadequate,
homogeneous, and most of algebraic knots and links. In the process of the proof
of main theorem, Gabai's Murasugi sum theorem is extended to the case of
nonorientable spanning surfaces.
