Galois theory of simple rings

Nakayama, Tadasi

doi:10.1090/S0002-9947-1952-0049875-3

Galois theory of simple rings
HTML articles powered by AMS MathViewer

by Tadasi Nakayama

Trans. Amer. Math. Soc. 73 (1952), 276-292

DOI: https://doi.org/10.1090/S0002-9947-1952-0049875-3

PDF | Request permission

References

Emil Artin and George Whaples, The theory of simple rings, Amer. J. Math. 65 (1943), 87–107. MR 7391, DOI 10.2307/2371775
Gorô Azumaya, New foundation of the theory of simple rings, Proc. Japan Acad. 22 (1946), no. 11, 325–332. MR 42387
Gorô Azumaya, Galois theory for uni-serial rings, J. Math. Soc. Japan 1 (1949), 130–146. MR 33277, DOI 10.2969/jmsj/00120130
Reinhold Baer, A Galois theory of linear systems over commutative fields, Amer. J. Math. 62 (1940), 551–588. MR 2857, DOI 10.2307/2371468
Henri Cartan, Théorie de Galois pour les corps non commutatifs, Ann. Sci. École Norm. Sup. (3) 64 (1947), 59–77 (French). MR 0023237
Jean Dieudonné, La théorie de Galois des anneaux simples et semi-simples, Comment. Math. Helv. 21 (1948), 154–184 (French). MR 24892, DOI 10.1007/BF02568032
G. Hochschild, Automorphisms of simple algebras, Trans. Amer. Math. Soc. 69 (1950), 292–301. MR 37834, DOI 10.1090/S0002-9947-1950-0037834-4
N. Jacobson, The fundamental theorem of the Galois theory for quasi-fields, Ann. of Math. (2) 41 (1940), 1–7. MR 1219, DOI 10.2307/1968817
N. Jacobson, A note on division rings, Amer. J. Math. 69 (1947), 27–36. MR 20981, DOI 10.2307/2371651
N. Jacobson, On the theory of primitive rings, Ann. of Math. (2) 48 (1947), 8–21. MR 19591, DOI 10.2307/1969211
Tadasi Nakayama, Note on irreducible rings, Proc. Japan Acad. 22 (1946), no. 11, 333–337. MR 42388
Tadasi Nakayama, Galois theory for general rings with minimum condition, J. Math. Soc. Japan 1 (1949), 203–216. MR 37283, DOI 10.2969/jmsj/00130203
Tadasi Nakayama, Generalized Galois theory for rings with minimum condition, Amer. J. Math. 73 (1951), 1–12. MR 40279, DOI 10.2307/2372153
Tadasi Nakayama, Automorphisms of simple, complete primitive, and directly indecomposable rings, Ann. of Math. (2) 55 (1952), 538–551. MR 47623, DOI 10.2307/1969647
Tadasi Nakayama, On derivation and cohomology in simple and other rings. I, Duke Math. J. 19 (1952), 51–63. MR 45704
Tadasi Nakayama and Gorô Azumaya, On irreducible rings, Ann. of Math. (2) 48 (1947), 949–965. MR 24891, DOI 10.2307/1969388
Kenjiro Shoda, Über die Galoissche Theorie der halbeinfachen hyperkomplexen Systeme, Math. Ann. 107 (1933), no. 1, 252–258 (German). MR 1512799, DOI 10.1007/BF01448892
Oswald Teichmüller, Über die sogenannte nichtkommutative Galoissche Theorie und die Relation $\xi _{\lambda ,\mu ,\nu }\xi _{\lambda ,\mu \nu ,\pi }\xi ^{\lambda }_{\mu ,\nu ,\pi }=\xi _{\lambda ,\mu ,\nu \pi }\xi _{\lambda ,\mu ,\nu ,\pi }$, Deutsche Math. 5 (1940), 138–149 (German). MR 2858