Editing Emmy Noether (section)

====Work in abstract algebra====
Although Noether's theorem had a significant effect upon classical and quantum mechanics, among mathematicians she is best remembered for her contributions to [[abstract algebra]]. In his introduction to Noether's ''Collected Papers'', [[Nathan Jacobson]] wrote that<blockquote>The development of abstract algebra, which is one of the most distinctive innovations of twentieth century mathematics, is largely due to her&nbsp;— in published papers, in lectures, and in personal influence on her contemporaries.{{sfn|Noether|1983}}</blockquote>

Noether's work in algebra began in 1920 when, in collaboration with her protégé Werner Schmeidler, she published a paper about the [[ideal theory|theory of ideals]] in which they defined [[Ideal (ring theory)|left and right ideals]] in a [[ring (mathematics)|ring]].{{sfn|Rowe|Koreuber|2020|p=27}}

The following year she published the paper ''Idealtheorie in Ringbereichen'',{{Sfn | Noether | 1921}} analyzing [[ascending chain condition]]s with regards to (mathematical) [[Ideal (ring theory)|ideals]], in which she proved the [[Lasker–Noether theorem]] in its full generality. Noted algebraist [[Irving Kaplansky]] called this work "revolutionary".{{Sfn |Kimberling|1981|p=18}} The publication gave rise to the term ''[[Noetherian]]'' for objects which satisfy the ascending chain condition.{{Sfn|Kimberling|1981|p=18}}{{Sfn|Dick|1981|pp=44–45}}

[[File:ETH-BIB-Waerden, Bartel Leendert van der (1903-1996)-Portr 12109.tif|thumb|230x230px|[[Bartel Leendert van der Waerden|B. L. van der Waerden]] (pictured in 1980) was heavily influenced by Noether at Göttingen.]]
In 1924, a young Dutch mathematician, [[Bartel Leendert van der Waerden]], arrived at the University of Göttingen. He immediately began working with Noether, who provided invaluable methods of abstract conceptualization. Van der Waerden later said that her originality was "absolute beyond comparison".{{Sfn|van der Waerden|1935}} After returning to Amsterdam, he wrote ''[[Moderne Algebra]]'', a central two-volume text in the field; its second volume, published in 1931, borrowed heavily from Noether's work.<ref name="Mactutor Biography"/> Although Noether did not seek recognition, he included as a note in the seventh edition "based in part on lectures by [[Emil Artin|E. Artin]] and E. Noether".{{Sfn|Lederman|Hill|2004|p=74}}{{Sfn|Dick|1981|pp=57–58}}{{Sfn|Kimberling|1981|p=19}} Beginning in 1927, Noether worked closely with [[Emil Artin]], [[Richard Brauer]] and [[Helmut Hasse]] on [[noncommutative algebra]]s.{{sfn |Weyl| 1935}}<ref name="Mactutor Biography"/>

Van der Waerden's visit was part of a convergence of mathematicians from all over the world to Göttingen, which had become a major hub of mathematical and physical research. Russian mathematicians [[Pavel Alexandrov]] and [[Pavel Urysohn]] were the first of several in 1923.{{Sfn|Kimberling|1981|p=24}} Between 1926 and 1930, Alexandrov regularly lectured at the university, and he and Noether became good friends.{{Sfn|Kimberling|1981|pp=24–25}} He dubbed her ''der Noether'', using ''der'' as an epithet rather than as the masculine German article.{{efn|The nickname was not always used in a well-meaning manner.{{sfn|Rowe|Koreuber|2020|p=14}} In Noether's obituary, Hermann stated that <blockquote>The power of your genius seemed to transcend the bounds of your sex, which is why we in Göttingen, in awed mockery, often spoke of you in the masculine form as "der Noether."{{sfn|Weyl|1935}}{{sfn|Rowe|Koreuber|2020|p=214}}</blockquote>}}{{Sfn|Kimberling|1981|pp=24–25}} She tried to arrange for him to obtain a position at Göttingen as a regular professor, but was able only to help him secure a scholarship to [[Princeton University]] for the 1927–1928 academic year from the [[Rockefeller Foundation]].{{Sfn|Kimberling|1981|pp=24–25}}{{Sfn|Dick|1981|pp=61–63}}