Ernst Steinitz entered the University of Breslau in 1890. He went to Berlin to study mathematics there in 1891 and, after spending two years in Berlin, he returned to Breslau in 1893. In the following year Steinitz submitted his doctoral thesis to Breslau and, the following year, he was appointed Privatdozent at the Technische Hochschule Berlin - Charlottenburg. The offer of a professorship at the Technical College of Breslau saw him return to Breslau in 1910. Ten years later he moved to Kiel where he was appointed to the chair of mathematics at the University of Kiel.
Steinitz was a friend of Toeplitz. The direction of his mathematics was also much influenced by Heinrich Weber and by Hensel's results on p-adic numbers in 1899. In [2] interesting results by Steinitz are discussed. These results were given by Steinitz in 1900, when he was a Privatdozent at the Technische Hochschule Berlin - Charlottenburg, at the annual meeting of the Deutsche Mathematiker-Vereinigung in Aachen. In his talk Steinitz introduced an algebra over the ring of integers whose base elements are isomorphism classes of finite abelian groups. Today this is known as the Hall algebra. Steinitz made a number of conjectures which were later proved by Hall.
Steinitz is most famous for work which he published in 1910. He gave the first abstract definition of a field in "Algebraische Theorie der Kˆrper" in that year. Prime fields, separable elements and the degree of transcendence of an extension field are all introduced in this 1910 paper. He proved that every field has an algebraically closed extension field, perhaps his most important single theorem. The now standard construction of the rationals as equivalence classes of pairs of integers under the equivalence relation: (a,b) is equivalent to (c,d) if and only if ad = bc was also given by Steinitz in 1910. Steinitz also worked on polyhedra and his manuscript on the topic was edited by Rademacher in 1934 after his death.