In the third epoch, Emmy Noether focused on non-commutative algebras, and unified much earlier work on the representation theory of groups.
| Index | Year | Title and English translation | Journal, volume, pages | Classification and notes |
| 32 | 1927 | Der Diskriminantensatz für die Ordnungen eines algebraischen Zahl- oder Funktionenkörpers | The Discriminant theorem for the Orders of an Algebraic Number Field or Function Field§ | | Journal für die reine und angewandte Mathematik, 157, 82–104 | Group representations, modules and ideals. Second of four papers showing the close connection between these three subjects. See also publications , , and . |
| 33 | 1927 | Über minimale Zerfällungskörper irreduzibler Darstellungen | On the Minimum Splitting Fields of Irreducible Representations§ | | Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1927, 221–228 | Group representations, modules and ideals. Written with R. Brauer. Third of four papers showing the close connection between these three subjects. See also publications , , and . This paper shows that the splitting fields of a division algebra are embedded in the algebra itself; the splitting fields are maximal commutative subfields either over the algebra, or over a full matrix ring over the algebra. |
| 34 | 1928 | Hyperkomplexe Größen und Darstellungstheorie, in arithmetischer Auffassung | Hypercomplex Quantities and the Theory of Representations, from an Arithmetic Perspective§ | | Atti Congresso Bologna, 2, 71–73 | Group representations, modules and ideals. Synopsis of her papers showing the close connection between these three subjects. See also publications , , , and . |
| 35 | 1929 | Hyperkomplexe Größen und Darstellungstheorie | Hypercomplex Quantities and the Theory of Representations | | Mathematische Zeitschrift, 30, 641–692 | Group representations, modules and ideals. Final paper of four showing the close connection between these three subjects. See also publications , , and . |
| 36 | 1929 | Über Maximalbereiche von ganzzahligen Funktionen | On the Maximal Domains of Integral Functions§ | | Rec. Soc. Math. Moscou, 36, 65–72 | |
| 37 | 1929 | | Differents and Ideal Differentiation§ | | Jahresbericht der Deutschen Mathematiker-Vereinigung, 39 (Abt. 2), 17 | |
| 38 | 1932 | Normalbasis bei Körpern ohne höhere Verzweigung | Normal Basis in Fields without Higher Ramification§ | | Journal für die reine und angewandte Mathematik, 167, 147–152 | |
| 39 | 1932 | Beweis eines Hauptsatzes in der Theorie der Algebren | Proof of a Main Theorem in the Theory of Algebras§ | | Journal für die reine und angewandte Mathematik, 167, 399–404 | Written with R. Brauer and H. Hasse. |
| 40 | 1932 | Hyperkomplexe Systeme in ihren Beziehungen zur kommutativen Algebra und zur Zahlentheorie | Hypercomplex Systems in Their Relationship to Commutative Algebra and to Number Theory§ | | Verhandl. Internat. Math. Kongress Zürich 1, 189–194 | |
| 41 | 1933 | Nichtkommutative Algebren | Non-commutative Algebras§ | | Mathematische Zeitschrift, 37, 514–541 | |
| 42 | 1933 | Der Hauptgeschlechtsatz für relativ-galoissche Zahlkörper | The Principal Genus Theorem for Relatively Galois Fields of Numbers§ | | Mathematische Annalen, 108, 411–419 | |
| 43 | 1934 | Zerfallende verschränkte Produkte und ihre Maximalordnungen, Exposés mathématiques publiés à la mémoire de J. Herbrand IV | Decomposing Crossed Products and Their Maximal Orders, in memory of J. Herbrand IV§ | | Actualités scient. et industr., 148 | |
| 44 | 1950 | Idealdifferentiation und Differente | Differents and Ideal Differentiation§ | | Journal für die reine und angewandte Mathematik, 188, 1–21 | |
