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Transactions of the American Mathematical Society

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Galois theory of continuous transformation rings


Authors: Alex Rosenberg and Daniel Zelinsky
Journal: Trans. Amer. Math. Soc. 79 (1955), 429-452
MSC: Primary 09.3X
DOI: https://doi.org/10.1090/S0002-9947-1955-0072121-4
MathSciNet review: 0072121
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  • [1] E. Artin, Galois theory, Notre Dame, 1942. MR 0006974 (4:66k)
  • [2] E. Artin and G. Whaples, The theory of simple rings, Amer. J. Math. vol. 65 (1943) pp. 87-102. MR 0007391 (4:129c)
  • [3] H. Cartan, Théorie de Galois pour les corps non commutatifs, Ann. École Norm. vol. 64 (1947) pp. 59-77. MR 0023237 (9:325f)
  • [4] J. Dieudonné, Sur le socle d'un anneau et les anneaux simples infinis, Bull. Soc. Math. France vol. 62 (1942) pp. 46-75. MR 0011289 (6:144a)
  • [5] -, La théorie de Galois des anneaux simples et semisimples, Comment. Math. Helv. vol. 21 (1948) pp. 154-184. MR 0024892 (9:563d)
  • [6] G. Hochschild, Automorphisms of simple algebras, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 292-301. MR 0037834 (12:315b)
  • [7] N. Jacobson, The theory of rings, Mathematical Surveys, No. 2, New York, 1943. MR 0008601 (5:31f)
  • [8] -, The radical and semi-simplicity for arbitrary rings, Amer. J. Math. vol. 67 (1945) pp. 300-320. MR 0012271 (7:2f)
  • [9] -, A note on division rings, Amer. J. Math. vol. 64 (1947) pp. 27-36. MR 0020981 (9:4c)
  • [10] -, On the theory of primitive rings, Ann. of Math. vol. 48 (1947) pp. 8-21. MR 0019591 (8:433a)
  • [11] -, Lectures in abstract algebra, vol. 2, New York, 1953.
  • [12] N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 479-502. MR 0038335 (12:387h)
  • [13] I. Kaplansky, Topological representations of algebras, Trans. Amer. Math. Soc. vol. 68 (1950) pp. 62-75. MR 0032612 (11:317c)
  • [14] W. Krull, Zur Theorie der allgemeinen Zahlringe, Math. Ann. vol. 99 (1928) pp. 51-70. MR 1512438
  • [15] T. Nakayama, Galois theory of simple rings, Trans. Amer. Math. Soc. vol. 73 (1952) pp. 276-292. MR 0049875 (14:240a)
  • [16] A. Rosenberg, Finite-dimensional simple subalgebras of the ring of all continuous linear transformations, Math. Zeit. vol. 61 (1954) pp. 150-159. MR 0066368 (16:563c)
  • [17] B. L. Van der Waerden, Moderne Algebra, vol. 2, Berlin, 1940.
  • [18] D. Zelinsky, Every linear transformation is the sum of nonsingular ones, Proc. Amer. Math. Soc. vol. 5 (1954) pp. 627-630. MR 0062728 (16:8c)

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DOI: https://doi.org/10.1090/S0002-9947-1955-0072121-4
Article copyright: © Copyright 1955 American Mathematical Society

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