## Kaete Hey and the Main Theorem in the theory of algebras.(English)Zbl 1154.01015

Wiȩsław, Witold (ed.), European mathematics in the last centuries. Lectures presented at the conference, Bȩdlewo, Poland, April 26–30, 2004. Wrocław: University of Wrocław, Institute of Mathematics (ISBN 83-89366-38-X/pbk). 57-76 (2005).
In a 1927 dissertation supervised by Emil Artin, Kaete Hey was the first to study zeta functions of algebraic skew fields. The author briefly discusses Hey’s dissertation, including the so-called “Main Theorem in the Theory of Algebras.” (If $$D$$ is a skew field over a field $$K$$ which splits at every place $$\mathfrak{p}$$ of $$K$$, the equivalence class of a nontrivial valuation on $$K$$, then $$D$$ splits over $$K$$.) Also discussed are some errors and subsequent corrections in Hey’s dissertation [M. Zorn, Abh. Math. Semin. Hamb. Univ. 9, 197–201 (1933; Zbl 0007.29701; JFM 59.0212.02)]. The dissertation appears to be her sole research-level contribution to mathematics. Some biographical details of her life are given in the paper.
For the entire collection see [Zbl 1108.01001].

### MSC:

 01A60 History of mathematics in the 20th century

### Keywords:

Skew field; zetafunction; valuation

### Citations:

Zbl 0007.29701; JFM 59.0212.02