Tadashi (or Tadasi) Nakayama (1912 - 1964)

1912, July born in Tokyo
1935 Graduated form Tokyo University.
Assistant professor at Osaka University
1937 Associate professor at Osaka University
1937 - 1939 stayed at Princeton
1941 Doctor of Science at Osaka University by the paper "On Frobenius algebras, I, II"
1942 Associate professor at Nagoya University
1944 Professor at Nagoya University
1947 He won a prize called "Chunichi Bunkashou" together with G. Azumaya
1948 - 1949 Illinois University
1953 He won a prize, from the Japan Academy, called "Gakushi-in shou" (one of the most important prizes in Japan.)
1953 - 1955 Hamburg University, Princeton
1963 Member of the Japan Academy
1964 Death in Nagoya

Tadasi Nakayama was born in Tokyo in July 1912. It is said that his father was an eminent scholar of Chinese classics. He graduated from Musasi high school under the old system and from the (Imperial) University of Tokyo.

It is not clear who was his superviser at Tokyo University. He learned algebra by very carefully reading Kenjiro Shoda's book "Abstract Algebra" and he published some papers solving some problems posed in the book. Shoda, an uncle of an empress, was a mathematician who founded the department of Mathematics in Osaka University. He learned abstract algebra from E. Noether in Goettingen - Shoda was one of the Noether boys.

In 1935 soon after the graduation of university he had a job as a Research Associate at the University of Osaka that was founded shortly before that. In 1937 he became an Associate Professor there. He stayed there for seven years until moving to the newly founded University of Nagoya in 1942 as an Associate Professor.

Inbetween from September 1937 he stayed for two years at Institute of Princeton He was 25 years at that time and he was the first Japanese who stayed for a longer period at Princeton. At that time, he met Brauer, Artin, Nesbitt, and Chevalley.

During that stay he visited Brauer in Toronto twice. He was impressed to see so many examples and calculations on representation theory in Brauer's office, and to know they were behind the beautiful theory. He was often in contact with Brauer and this gave him a decisive influence on his study. Brauer-Nesbitt published their first paper on modular representations in 1937, and then Nakayama published a paper on "Frobenius-Nakayama reciprocal law" in 1938. The influence on Brauer can also be seen when he started the study on Frobeniusean algebras in Princeton or in his paper on modular representations of symmetric groups published in 1940, in which beautiful theorems and conjectures were derived from complicated calculations. He once mentioned a conversation with Brauer, who told him that he (Brauer) wanted to quit studying algebra. When Nakayama asked what else he would like to do, Brauer replied: "Topology".

In 1941 he got Doctor of Science at the University of Osaka with the papers "On Frobeniusean algebras, I, II".

He was working at Nagoya University from 1942. In 1944 he became a full Professor at the University of Nagoya. Joint work with Goro Azumaya produced a lot of excellent results on representation theory of algebras. He published a book "Algebra II" with G. Azumaya, which includes in its second half (written by Azumaya) many of their joint results on Frobenius algebras, quasi-Frobenius algebras, and symmetric algebras. Nakayama wrote the first half on the structure of rings, which is similar to Jacobson's book.

Before his travel to Princeton in 1937, he had already contracted tuberculosis. Of course, in those days, one had to undergo very strict physical examinations when going abroad. The reason why he passed the medical check was that he could get a doctor's report not mentioning his T.B.. (A rumour claims that the doctor was his relative.) Many people have regretted this report: If the doctor had reported correctly, then Nakayama would not have died so early. Before his death, there were chairs at each floor at the department of mathematics in Nagoya University so that Nakayama could take a rest. While he was ill (T.B.) in bed, he was learning Grothendieck's approach towards Algebraic Geometry. People say that he made the sickness worse through overwork.

In 1947 he won the Price of Culture in the Middle Area of Japan with Goro Azumaya. He stayed at the University of Illinois from 1948 to 1949. In 1953 he won the Japan Academy Award. From 1953 to 1955 he stayed at the University of Hamburg and at the Institute of Princeton. In 1963 he became a member of Japan Academy.

In 1964 he died by tuberculosis.

Nakayama obtained great results on modular representations of symmetric groups, quasi-Frobenius rings, Frobenius extensions, Galois theory of rings, and he also was interested in class field theory.

Some papers:

About the Nakayama lemma: