Direct decompositions of Galois algebras
Katsuhiko Masuda · Tohoku Mathematical Journal · 1952
In his article "Invariante Kennzeichnung Galoisscher Kδrper mit vorgegebener Galoisgruppe" x) H. Hasse established the important concepts of Galois algebras and factor systems. (We call them in the following respectively Hasse's Galois algebras and Hasse factor systems.)The aim of the present article is to give a characterization of those Hasse factor systems which are associated with Galois fields.We define Galois algebras more generally than Hasse, as T.Nakayama did 2) , and introduce matrix systems associated with them.The generalization simplifies the calculations necessary to solve the above stated problem about Hasse factor systems.The present work was done while I was a student of Prof. T. Tannaka and I wish to acknowledge my deep indebtedness to him.