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Celebratio Mathematica

Emmy Noether

Algebra

Bibliography

[1]E. No­eth­er: Über die Bildung des For­mensys­tems der ternären bi­quad­rat­ischen Form [On com­plete sys­tems of in­vari­ants for tern­ary bi­quad­rat­ic forms]. Ph.D. thesis, Friedrich-Al­ex­an­der-Uni­versität Er­lan­gen-Nürn­berg, December 1907. Ad­vised by P. A. Gordan.

[2]E. No­eth­er: “Über die Bildung des For­mensys­tems der ternären bi­quad­rat­ischen Form” [On com­plete sys­tems of in­vari­ants for tern­ary bi­quad­rat­ic forms], Sitz. Ber. Phys.-Med. Soz. Er­lan­gen 39 (1907), pp. 176–​179. Pre­lim­in­ary four-page re­port on the au­thor’s Ph.D. dis­ser­ta­tion res­ults.

[3]E. No­eth­er: “Über die Bildung des For­mensys­tems der ternären bi­quad­rat­ischen Form” [On com­plete sys­tems of in­vari­ants for tern­ary bi­quad­rat­ic forms], J. Reine An­gew. Math. 134 (1908), pp. 23–​90. Main de­scrip­tion of au­thor’s dis­ser­ta­tion.

[4]E. No­eth­er: “Zur In­vari­anten­the­or­ie der For­men von \( n \) Variabeln” [On the the­ory of in­vari­ants for forms of \( n \) vari­ables], Jahresber. Deutsch. Math.-Ver­ein. 19 (1910), pp. 101–​104. JFM 41.​0149.​01 article

[5]E. No­eth­er: “Zur In­vari­anten­the­or­ie der For­men von \( n \) Variabeln” [On the the­ory of in­vari­ants for forms of \( n \) vari­ables], J. Reine An­gew. Math. 139 (1911), pp. 118–​154. JFM 41.​0149.​02 article

[6]E. No­eth­er: “Ra­tionale Funk­tion­en­körp­er” [Ra­tion­al func­tion fields], Jahresber. Deutsch. Math.-Ver­ein. 22 (1913), pp. 316–​319. JFM 44.​0496.​02 article

[7]E. No­eth­er: “Körp­er und Systeme ra­tionaler Funk­tion­en” [Fields and sys­tems of ra­tion­al func­tions], Math. Ann. 76 : 2–​3 (1915), pp. 161–​196. MR 1511817 JFM 46.​1442.​08 article

[8]E. No­eth­er: “Die allge­mein­sten Bereiche aus gan­zen transzenden­ten Zah­len” [The most gen­er­al do­mains of com­pletely tran­scend­ent­al num­bers], Math. Ann. 77 : 1 (1915), pp. 103–​128. MR 1511850 JFM 45.​0163.​02 article

[9]E. No­eth­er: “Der End­lich­keits­satz der In­vari­anten end­lich­er Grup­pen” [The fi­nite­ness the­or­em for in­vari­ants of fi­nite groups], Math. Ann. 77 : 1 (1915), pp. 89–​92. MR 1511848 JFM 45.​0198.​01 article

[10]E. No­eth­er: “Über gan­ze ra­tionale Darstel­lung der In­vari­anten eines Sys­tems von be­liebig vielen Grund­for­men” [On an in­teg­ral ra­tion­al rep­res­ent­a­tion of the in­vari­ants of a sys­tem of ar­bit­rar­ily many basis forms], Math. Ann. 77 : 1 (1915), pp. 93–​102. JFM 45.​0197.​02 article

[11]E. No­eth­er: “Die Funk­tion­algleichun­gen der iso­morph­en Ab­bildung” [Func­tion­al equa­tions of the iso­morph­ic map­ping], Math. Ann. 77 : 4 (1916), pp. 536–​545. MR 1511878 JFM 46.​0170.​02 article

[12]E. No­eth­er: “Gleichun­gen mit vorges­chrieben­er Gruppe” [Equa­tions with pre­scribed group], Math. Ann. 78 : 1–​4 (1917), pp. 221–​229. MR 1511893 JFM 46.​0135.​01 article

[13]E. No­eth­er and W. Schmeidler: “Mod­uln in nichtkom­mut­at­iven Bereichen, ins­beson­dere aus Dif­fer­en­tial- und Dif­fer­en­zenaus­drück­en” [Mod­ules in non-com­mut­at­ive do­mains, es­pe­cially those com­posed of dif­fer­en­tial and dif­fer­ence ex­pres­sions], Math. Z. 1 : 1 (1918), pp. 1–​35. MR 1544274 article

[14]E. No­eth­er: “In­vari­ante Vari­ation­sprob­leme” [In­vari­ant vari­ation­al prob­lems], Na­chr. Ges. Wiss. Gött., Math.-Phys. Kl. (1918), pp. 235–​257. JFM 46.​0770.​01 article

[15]E. No­eth­er: “In­vari­anten be­liebi­ger Dif­fer­en­tialaus­drücke” [In­vari­ants of ar­bit­rary dif­fer­en­tial ex­pres­sions], Na­chr. Ges. Wiss. Gött., Math.-Phys. Kl. 1918 (1918), pp. 37–​44. JFM 46.​0675.​01 article

[16]E. No­eth­er: “Die arith­met­ische The­or­ie der al­geb­rais­chen Funk­tion­en ein­er Ver­än­der­lichen in ihr­er Bez­iehung zu den übri­gen The­ori­en und zu der Zahlkörper­the­or­ie” [The arith­met­ic the­ory of al­geb­ra­ic func­tions of one vari­able in its re­la­tion­ship to the oth­er the­or­ies and to num­ber field the­ory], Jahresber. Deutsch. Math.-Ver­ein. 28 : 1 (1919), pp. 182–​203. JFM 47.​0349.​06 article

[17]E. No­eth­er: “Die End­lich­keit des Sys­tems der gan­zzah­li­gen In­vari­anten binärer For­men” [A proof of fi­nite­ness for in­teg­ral bin­ary in­vari­ants], Na­chr. Ges. Wiss. Gött., Math.-Phys. Kl. (1919), pp. 138–​156.

[18]E. No­eth­er: “Zur Reihen­entwicklung in der For­men­the­or­ie” [On series ex­pan­sions in the the­ory of forms], Math. Ann. 81 : 1 (1920), pp. 25–​30. Ad­di­tions and cor­rec­tions to “Über gan­ze ra­tionale Darstel­lung der In­vari­anten eines Sys­tems von be­liebig vielen grund­for­men,” Math. Ann. 77 (1915), pp. 93–102. MR 1511953 JFM 47.​0089.​01 article

[19]E. No­eth­er and W. Schmeidler: “Mod­uln in nichtkom­mut­at­iven Bereichen, ins­beson­dere aus Dif­fer­en­tial- und Dif­fer­en­zenaus­drück­en” [Mod­ules in non-com­mut­at­ive do­mains, es­pe­cially those com­posed of dif­fer­en­tial and dif­fer­ence ex­pres­sions], Math. Z. 8 : 1–​2 (1920), pp. 1–​35. MR 1544424 JFM 47.​0097.​03 article

[20]E. No­eth­er: “Ideal­the­or­ie in Ringbereichen” [The the­ory of ideals in ring do­mains], Math. Ann. 83 : 1–​2 (1921), pp. 24–​66. MR 1511996 JFM 48.​0121.​03 article

[21]E. No­eth­er: “Über eine Arbeit des im Kriege ge­fallen­en K. Hentzelt zur Elim­in­a­tion­s­the­or­ie” [On a work on elim­in­a­tion the­ory by K. Hentzelt, who fell in the War], Jahresber. Deutsch. Math.-Ver­ein. 30 : 2 (1921), pp. 101. JFM 48.​0094.​02 article

[22]E. No­eth­er: “For­m­ale Vari­ation­srech­nung und Dif­fer­en­tial­in­vari­anten” [Form­al cal­cu­lus of vari­ations and dif­fer­en­tial in­vari­ants], pp. 68–​71 in R. Weitzenböck: Neuere Arbeiten der al­geb­rais­chen In­vari­anten­the­or­ie. Dif­fer­en­tial­in­vari­anten. En­cyc­lopädie der math­em­at­ischen Wis­senschaften III, 3, E. 1921.

[23]K. Hentzelt and E. No­eth­er: “Zur The­or­ie der Poly­nom­ideale und Res­ult­anten” [On the the­ory of poly­no­mi­al ideals and res­ult­ants], Math. Ann. 88 : 1–​2 (1922), pp. 53–​79. MR 1512119 JFM 48.​0094.​03 article

[24]E. No­eth­er: “Ein al­geb­raisches Kri­teri­um für ab­so­lute Ir­re­duz­ib­il­ität” [An al­geb­ra­ic cri­terion for ab­so­lute ir­re­du­cib­il­ity], Math. Ann. 85 : 1 (1922), pp. 26–​40. MR 1512042 JFM 48.​0081.​03 article

[25]E. No­eth­er: “Elim­in­a­tion­s­the­or­ie und allge­meine Ideal­the­or­ie” [Elim­in­a­tion the­ory and the gen­er­al ideal the­ory], Math. Ann. 90 : 3–​4 (1923), pp. 229–​261. MR 1512173 JFM 49.​0076.​04 article

[26]E. No­eth­er: “Al­geb­rais­che und Dif­fer­en­tial­in­vari­anten” [Al­geb­ra­ic and dif­fer­en­tial in­vari­ants], Jahresber. Deutsch. Math.-Ver­ein. 32 (1923), pp. 177–​184. JFM 49.​0068.​01 article

[27]E. No­eth­er: “Elim­in­a­tion­s­the­or­ie und Ideal­the­or­ie” [Elim­in­a­tion the­ory and ideal the­ory], Jahresber. Deutsch. Math.-Ver­ein. 33 (1924), pp. 116–​120. JFM 50.​0071.​02 article

[28]E. No­eth­er: “Grup­pen­charaktere und Ideal­the­or­ie” [Group char­ac­ters and the the­ory of ideals], Jahresber. Deutsch. Math.-Ver­ein. 34 : 2 (1925), pp. 144. JFM 52.​0136.​04 article

[29]E. No­eth­er: “Der End­lich­keits­satz der In­vari­anten end­lich­er lin­ear­er Grup­pen der Charak­ter­istik \( p \)” [Proof of the fi­nite­ness of the in­vari­ants of fi­nite lin­ear groups of char­ac­ter­ist­ic \( p \)], Na­chr. Ges. Wiss. Gött., Math.-Phys. Kl. (1926), pp. 28–​35.

[30]E. No­eth­er: “Über min­i­male Zer­fäl­lung­skörp­er ir­re­duz­i­b­ler Darstel­lungen” [On the min­im­um split­ting fields of ir­re­du­cible rep­res­ent­a­tions], Sitz. Preuß. Akad. Wis­senschaften (1927), pp. 221–​228. JFM 53.​0116.​01 article

[31]E. No­eth­er: “Der Diskrim­in­antensatz für die Ord­nun­gen eines al­geb­rais­chen Zahl- oder Funk­tion­enkörpers” [The dis­crim­in­ant the­or­em for the or­ders of an al­geb­ra­ic num­ber field or func­tion field], J. Reine An­gew. Math. 157 (1927), pp. 82–​104.

[32]E. No­eth­er: “Ab­strak­ter Auf­bau der Ideal­the­or­ie in al­geb­rais­chen Zahl- und Funk­tion­en­kör­pern” [Ab­stract struc­ture of the the­ory of ideals in al­geb­ra­ic num­ber fields], Math. Ann. 96 : 1 (1927), pp. 26–​ –​61. MR 1512304 JFM 52.​0130.​01 article

[33]E. No­eth­er: “Hy­per­kom­plexe Größen und Darstel­lung­sthe­or­ie” [Hy­per­com­plex quant­it­ies and the the­ory of rep­res­ent­a­tions], Math. Z. 30 : 1 (1929), pp. 641–​692. MR 1545085 JFM 55.​0677.​01 article

[34]E. No­eth­er: “Über Max­im­al­bereiche von gan­zzah­li­gen Funk­tion­en” [On the max­im­al do­mains of in­teg­ral func­tions], Trans. Mo­scow Math. Soc. 36 (1929), pp. 65–​72.

[35]E. No­eth­er: “Hy­per­kom­plexe Größen und Darstel­lung­sthe­or­ie in arith­met­ischer Auffas­sung” [Hy­per­com­plex quant­it­ies and the the­ory of rep­res­ent­a­tions from an arith­met­ic per­spect­ive], pp. 71–​73 in Atti del Con­gresso In­ternazionale dei Matem­atici (Bo­logna, 3–10 Septem­ber, 1928), vol. 2. Edi­ted by N. Zanichelli. 1929.

[36]E. No­eth­er: “Nor­mal­bas­is bei Kör­pern ohne höhere Verz­wei­gung” [Nor­mal basis in fields without high­er rami­fic­a­tion], J. Reine An­gew. Math. 167 (1932), pp. 147–​152. JFM 58.​0172.​02 article

[37]E. No­eth­er: “Hy­per­kom­plexe Systeme in ihren Bez­iehun­gen zur kom­mut­at­iven Al­gebra und zur Zah­len­the­or­ie” [Hy­per­com­plex sys­tems in their re­la­tion­ship to com­mut­at­ive al­gebra and to num­ber the­ory], pp. 189–​194 in Ver­hand­lun­gen des In­ter­na­tionalen Math­em­atiker-Kon­gresses Zürich 1932 (Zürich, Septem­ber 4–12, 1932), vol. 1. Edi­ted by W. Sax­er. Orell Füss­li Ver­lag (Zürich), 1932. JFM 58.​0142.​02 incollection

[38]R. Brauer, H. Hasse, and E. No­eth­er: “Be­weis eines Hauptsatzes in der The­or­ie der Al­gebren” [On the proof of a fun­da­ment­al the­or­em in the the­ory of al­geb­ras], J. Reine An­gew. Math. 167 (1932), pp. 399–​404. Zbl 0003.​24404 article

[39]E. No­eth­er: “Der Haupt­geschlechts­satz für re­lat­iv-galois­sche Zahlkörp­er” [The prin­cip­al genus the­or­em for re­l­at­ively Galois fields of num­bers], Math. Ann. 108 : 1 (1933), pp. 411–​419. MR 1512857 Zbl 0007.​29501 article

[40]E. No­eth­er: “Nichtkom­mut­at­ive Al­gebra” [Non-com­mut­at­ive al­gebra], Math. Z. 37 : 1 (1933), pp. 514–​541. MR 1545411 Zbl 0007.​19702 article

[41]E. No­eth­er: Zer­fal­lende ver­s­chränkte Produkte und ihre Max­im­al­ord­nun­gen [De­com­pos­ing crossed products and their max­im­al or­ders]. Ac­tu­al­ités sci­en­ti­fiques et in­dus­tri­elles 148. Her­mann & Cie (Par­is), 1934. Ex­posés math­ématiques pub­liés à la mé­m­oire de Jacques Herbrand, IV. JFM 60.​0101.​04 book

[42]Briefwech­sel Can­tor–Dede­kind [The Can­tor–Dede­kind cor­res­pond­ence]. Edi­ted by E. No­eth­er and J. Cavaillès. Ac­tu­alités sci­en­ti­fiques et in­dus­tri­elles 518. Her­mann & Cie (Par­is), 1937.

[43]E. No­eth­er: “Idealdif­fer­en­ti­ation und Dif­fer­ente” [Dif­fer­ents and ideal dif­fer­en­ti­ation], J. Reine An­gew. Math. 188 (1950), pp. 1–​21. MR 0038337 Zbl 0039.​02601 article

[44]E. No­eth­er: “In­vari­ant vari­ation prob­lems,” Trans­port The­ory Stat­ist. Phys. 1 : 3 (1971), pp. 186–​207. Trans­la­tion of the Ger­man ori­gin­al from Na­chr. Akad. Wiss. Göt­tin­gen Math.-Phys. Kl. 2 (1918), pp. 235–257. MR 0406752 Zbl 0292.​49008 article

[45]E. No­eth­er: Ges­am­melte Abhand­lun­gen [Col­lec­ted pa­pers]. Edi­ted by N. Jac­ob­son. Spring­er (Ber­lin), 1983. With an in­tro­duc­tion by the ed­it­or and an in­tro­duct­ory ad­dress by P. S. Al­ex­an­drov. MR 703862 Zbl 0504.​01035 book

[46]B. L. van der Waer­den: Al­gebra, 5th edition, vol. 2. Spring­er (New York), 1991. Based in part on lec­tures by E. Artin and E. No­eth­er. MR 1080173 Zbl 1032.​00002 book

[47]B. L. van der Waer­den: Al­gebra, 7th edition, vol. 1. Spring­er (New York), 1991. Based in part on lec­tures by E. Artin and E. No­eth­er. MR 1080172 Zbl 0039.​00902 book

[48]Helmut Hasse und Emmy No­eth­er: Die Kor­res­pondenz 1925–1935 [Helmut Hasse and Emmy No­eth­er: their cor­res­pond­ence 1925–1935]. Edi­ted by F. Lem­mer­mey­er and P. Ro­quette. Uni­versitäts­ver­lag Göt­tin­gen, 2006. With com­ment­ary and Eng­lish in­tro­duc­tion by the ed­it­ors. MR 2229240 Zbl 1101.​01010 book