"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."
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Immigrants to the United StatesAcademics from AustriaPrinceton University facultyMathematicians from AustriaUniversity of Notre Dame faculty
Original Language: English
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(quote from p. 67)
https://en.wikiquote.org/wiki/Emil_Artin
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Emil Artin
(March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. He is known for his research on modern , . and s.
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