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Topological representation of algebras


Authors: Richard F. Arens and Irving Kaplansky
Journal: Trans. Amer. Math. Soc. 63 (1948), 457-481
MSC: Primary 09.1X
DOI: https://doi.org/10.1090/S0002-9947-1948-0025453-6
MathSciNet review: 0025453
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  • [1] R. Arens, Representation of Banach $ \ast $-algebras, Duke Math. J. vol. 14 (1947) pp. 269-282. MR 0021250 (9:44b)
  • [2] -, Linear topological division algebras, Bull. Amer. Math. Soc. vol. 53 (1947) pp. 623-630. MR 0020987 (9:6a)
  • [3] E. Artin and G. Whaples, The theory of simple rings, Amer. J. Math. vol. 65 (1943) pp. 87-107. MR 0007391 (4:129c)
  • [4] B. Brown and N. H. McCoy, Radicals and subdirect sums, Amer. J. Math. vol. 69 (1947) pp. 46-58. MR 0019594 (8:433d)
  • [5] A. Forsythe and N. H. McCoy, The commutativity of certain rings, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 523-526. MR 0016093 (7:509g)
  • [6] I. Gelfand, Normierte ringe, Rec. Math. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 1-23. MR 0004726 (3:51f)
  • [7] I. Gelfand and M. Neumark, On the imbedding of normed rings into the ring of operators in Hilbert space, Rec. Math. (Mat. Sbornik) N.S. vol. 12 (1943) pp. 197-213. MR 0009426 (5:147d)
  • [8] W. Hurewicz and H. Wallman, Dimension theory, Princeton, 1941. MR 0006493 (3:312b)
  • [9] N. Jacobson, Theory of rings, Mathematical Surveys, vol. 2, American Mathematical Society, New York, 1943. MR 0008601 (5:31f)
  • [10] -, The radical and semi-simplicity for arbitrary rings, Amer. J. Math. vol. 67 (1945) pp. 300-320. MR 0012271 (7:2f)
  • [11] -, Structure theory of simple rings without finiteness assumptions, Trans. Amer. Math. Soc. vol. 57 (1945) pp. 228-245. MR 0011680 (6:200a)
  • [12] -, A topology for the set of primitive ideals in an arbitrary ring, Proc. Nat. Acad. Sci. U.S.A. vol. 31 (1945) pp. 333-338. MR 0013138 (7:110f)
  • [13] -, Structure theory for algebraic algebras of bounded degree, Ann. of Math. vol. 46 (1945) pp. 695-707. MR 0014083 (7:238c)
  • [14] R. E. Johnson and F. Kiokemeister, The endomorphisms of the total operator domain of an infinite module, Trans. Amer. Math. Soc. vol. 62 (1947) pp. 404-430. MR 0023811 (9:407f)
  • [15] I. Kaplansky, Topological methods in valuation theory, Duke Math. J. vol. 14 (1947) pp. 527-541. MR 0022210 (9:172f)
  • [16] -, Topological rings, Amer. J. Math. vol. 69 (1947) pp. 153-183. MR 0019596 (8:434b)
  • [17] S. Mazur, Sur les anneaux linéaires, C. R. Acad. Sci. Paris vol. 207 (1938) pp. 1025-1027.
  • [18] N. H. McCoy and D. Montgomery, A representation of generalized Boolean rings, Duke Math. J. vol. 3 (1937) pp. 455-459. MR 1546001
  • [19] N. H. McCoy, Subrings of direct sums, Amer. J. Math. vol. 60 (1938) pp. 374-382. MR 1507320
  • [20] J. v. Neumann, Regular rings, Proc. Nat. Acad. Sci. U.S.A. vol. 22 (1936) pp. 707-7713.
  • [21] I. E. Segal, The group algebra of a locally compact group, Trans. Amer. Math. Soc. vol. 61 (1947) pp. 69-105. MR 0019617 (8:438c)
  • [22] M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. vol. 40 (1936) pp. 37-111. MR 1501865
  • [23] -Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. vol. 41 (1937) pp. 375-481. MR 1501905

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DOI: https://doi.org/10.1090/S0002-9947-1948-0025453-6
Article copyright: © Copyright 1948 American Mathematical Society

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