Emil Artin

"The essential point in the definition of an algebra is that it is a vector space of finite dimension over a field. This fact allows us to conclude that of subalgebras will terminate. After the great success that Emmy Noether had in her ideal theory in rings with ascending chain condition, it seemed reasonable to expect that in rings where the ascending and the descending chain condition holds for left ideals one should obtain results similar to those of . As one of the papers written from this point of view we mention E. Artin, Zur Theorie der hyperkomplexen Zahlen (Abh. Math. Sem. Hamburgischen Univ. vol. 5 (1926)). In 1939 showed (Rings with minimal condition f or left ideals, Ann. of Math. vol. 40) that the descending chain condition suffices."

"I think he would have made a great actor. His lectures were polished: He would finish at the right moment and march off the scene. A very lively individual with many interests: music, astronomy, chemistry, history.... He loved to teach. I had a feeling that he loved to teach anybody anything. Being his student was a wonderful experience; I couldn’t have had a better start to my mathematical career. It was a remarkable accident. My favorite theorem, which I had first learned from Bell’s book, was Gauss’s law of , and there, entirely by chance, I found myself at the same university as the man who had discovered the . It was just amazing."