Steinitz's 1894 thesis was on the subject of
projective configurations; it contained the result that any abstract description of an
incidence structure of three lines per point and three points per line could be realized as a configuration of straight lines in the
Euclidean plane with the possible exception of one of the lines. His thesis also contains the proof of
Kőnig's theorem for
regular bipartite graphs, phrased in the language of configurations. In 1910 Steinitz published the very influential paper
Algebraische Theorie der Körper (
German: Algebraic Theory of Fields, ''
Crelle's Journal). In this paper he axiomatically studies the properties of fields and defines important concepts like prime field, perfect field and the transcendence degree of a field extension, and also normal and separable extensions (the latter he called algebraic extensions of the first kind''). Besides numerous, today standard, results in
field theory, he proved that every field has an (essentially unique)
algebraic closure and a theorem, which characterizes the
existence of primitive elements of a field extension in terms of its intermediate fields.
Bourbaki called this article "a basic paper which may be considered as having given rise to the current conception of Algebra". Steinitz also made fundamental contributions to the theory of
polyhedra:
Steinitz's theorem for polyhedra is that the 1-
skeletons of
convex polyhedra are exactly the 3-
connected planar graphs. His work in this area was published posthumously as a 1934 book,
Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie, by
Hans Rademacher. == See also ==