Galois theory of continuous transformation rings

Galois theory of continuous transformation rings
HTML articles powered by AMS MathViewer

Trans. Amer. Math. Soc. 79 (1955), 429-452

DOI: https://doi.org/10.1090/S0002-9947-1955-0072121-4

PDF | Request permission

References

Emil Artin, Galois Theory, Notre Dame Mathematical Lectures, no. 2, University of Notre Dame, Notre Dame, Ind., 1942. Edited and supplemented with a section on applications by Arthur N. Milgram. MR 0006974
Emil Artin and George Whaples, The theory of simple rings, Amer. J. Math. 65 (1943), 87–107. MR 7391, DOI 10.2307/2371775
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, Sur le socle d’un anneau et les anneaux simples infinis, Bull. Soc. Math. France 70 (1942), 46–75 (French). MR 11289
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
Nathan Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys, Vol. II, American Mathematical Society, New York, 1943. MR 0008601
N. Jacobson, The radical and semi-simplicity for arbitrary rings, Amer. J. Math. 67 (1945), 300–320. MR 12271, DOI 10.2307/2371731
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

Lectures in abstract algebra

N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), 479–502. MR 38335, DOI 10.1090/S0002-9947-1950-0038335-X
Irving Kaplansky, Topological representation of algebras. II, Trans. Amer. Math. Soc. 68 (1950), 62–75. MR 32612, DOI 10.1090/S0002-9947-1950-0032612-4
Wolfgang Krull, Zur Theorie der allgemeinen Zahlringe, Math. Ann. 99 (1928), no. 1, 51–70 (German). MR 1512438, DOI 10.1007/BF01459085
Tadasi Nakayama, Galois theory of simple rings, Trans. Amer. Math. Soc. 73 (1952), 276–292. MR 49875, DOI 10.1090/S0002-9947-1952-0049875-3
Alex Rosenberg, Finite-dimensional simple subalgebras of the ring of all continuous linear transformations, Math. Z. 61 (1954), 150–159. MR 66368, DOI 10.1007/BF01181339

Moderne Algebra

Daniel Zelinsky, Every linear transformation is a sum of nonsingular ones, Proc. Amer. Math. Soc. 5 (1954), 627–630. MR 62728, DOI 10.1090/S0002-9939-1954-0062728-7