Bulletin of the American Mathematical Society

Author(s): Irving Kaplansky
Journal: Bull. Amer. Math. Soc. 54 (1948), 809-826.
MathSciNet review: 0026643
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3.: W. Ambrose, The L2-system of a unimodular group, To be published in Trans. Amer. Math. Soc. MR 28322
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21.: M. Freundlich, On normed rings, Dissertation, Illinois, 1947.
22.: I. Gelfand, Normierte Ringe, Rec. Math. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 3-24. MR 4726
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24.: I. Gelfand, Zur Theorie der Charaktere der abelschen topologischen Gruppen, Rec. Math. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 49-50. MR 4635
25.: I. Gelfand, Über absolut konvergente trigonometrische Reihen und Integrale, Rec. Math. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 51-66. MR 4727
26.: 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 9426
27.: I. Gelfand and D. Raikov, On the theory of characters of commutative topological groups, C. R. (Doklady) Acad. Sci. URSS. vol. 28 (1940) pp. 195-198. MR 3423
28.: I. Gelfand and D. Raikov, Irreducible unitary representations of locally compact groups, Rec. Math. (Mat. Sbornik) N.S. vol. 13 (1943) pp. 301-316. MR 11308
29.: R. Godement, Les fonctions de type positif et la théorie des groupes, Trans. Amer. Math. Soc. vol. 63 (1948) pp. 1-84. MR 23243
30.: R. Godement, Théorèmes taubériens et théorie spectrale, Ann. École Norm. vol. 74 (1947) pp. 119-138. MR 23242
31.: W. Habicht, Ein Existenzsatz über reele definite Polynome, Comment. Math. Helv. vol. 18 (1946) pp. 331-348. MR 16747
32.: P. Hebroni, Über lineare Differentialgleichungen in Ringen, Compositio Math. vol. 5 (1938) pp. 403-429. MR 1557008
33.: E. Hewitt, On rings of continuous real-valued functions, Trans. Amer. Math. Soc. vol. 64 (1948) pp. 45-99. MR 26239
34.: D. Hyers, Linear topological spaces, Bull. Amer. Math. Soc. vol. 51 (1945) pp. 1-21. MR 12205
35.: N. Jacobson and O. Taussky, Locally compact rings, Proc. Nat. Acad. Sci. U. S. A. vol. 21 (1935) pp. 106-108.
36.: N. Jacobson, Totally disconnected locally compact rings, Amer. J. Math. vol. 58 (1936) pp. 433-449. MR 1507166
37.: N. Jacobson, A note on topological fields, Amer. J. Math. vol. 59 (1937) pp. 889-894. MR 1507289
38.: N. Jacobson, The radical and semi-simplicity for arbitrary rings, Amer. J. Math. vol. 67 (1945) pp. 300-320. MR 12271
39.: I. Kaplansky, Maximal fields with valuations, Duke Math. J. vol. 9 (1942) pp. 303-321, vol. 12 (1945) pp. 243-248. MR 6161
40.: I. Kaplansky, Topological rings, Amer. J. Math. vol. 69 (1947) pp. 153-183. MR 19596
41.: I. Kaplansky, Topological methods in valuation theory, Duke Math. J. vol. 14 (1947) pp. 527-541. MR 22210
42.: I. Kaplansky, Polynomials in topological fields, To be published in Bull. Amer. Math. Soc. MR 27269
43.: I. Kaplansky, Dual rings Ann. of Math. vol. 49 (1948) pp. 689-701. MR 25452
44.: I. Kaplansky, Locally compact rings, Amer. J. Math. vol. 70 (1948) pp. 447-459. MR 24887
45.: I. Kaplansky, Regular Banach algebras, To appear in J. Indian Math. Soc. MR 29106
46.: I. Kaplansky, Normed algebras, in preparation.
47.: I. Kapuano, Sur les corps de nombres a une dimension distincts du corps réel, Rev. Fac. Sci. Univ. Istanbul (A) vol. 11 (1946) pp. 30-39. MR 16649
48.: Y. Kawada, Über die Erweiterung der maximalen Ideale in normierten Ringen, Proc. Imp. Acad. Tokyo vol. 19 (1943) pp. 267-268. MR 14582
49.: K. Kodaira and S. Kakutani, Normed ring of a locally compact abelian group, Proc. Imp. Acad. Tokyo vol. 19 (1943) pp. 360-365. MR 14094
50.: A. Kolmogoroff, Zur Begründung der projektiven Geometrie, Ann. of Math. vol. 33 (1932) pp. 175-176. MR 1503044
51.: G. Köthe, Abstrakte Theorie nichtkommutativer Ringe mit einer Anwendung auf die Darstellungstheorie kontinuierlicher Gruppen, Math. Ann. vol. 103 (1930) pp. 545-572. MR 1512637
52.: G. Köthe, Unendliche abelsche Gruppen und Grundlagen der Geometrie, Jber. Deutschen Math. Verein. vol. 49 (1939) pp. 97-113. MR 813
53.: W. Krull, Allgemeine Bewertungstheorie, Journal für Mathematik vol. 167 (1932) pp. 160-196.
54.: J. Kürschak, Über Limesbildung und allgemeine Körpertheorie, Journal für Mathematik vol. 142 (1913) pp. 211-253.
55.: E. Lorch, The structure of normed abelian rings, Bull. Amer. Math. Soc. vol. 50 (1944) pp. 447-463. MR 10780
56.: S. MacLane, Subfields and automorphism groups of p-adic fields, Ann. of Math. vol. 40 (1939) pp. 423-442. MR 1503470
57.: F. Mautner, The completeness of the irreducible unitary representations of a locally compact group, Proc. Nat. Acad. Sci. U. S. A. vol. 34 (1948) pp. 52-54. MR 23245
58.: S. Mazur, Sur les anneaux linéaires, C. R. Acad. Sci. Paris vol. 207 (1938) pp. 1025-1027.
59.: D. Milman, On the normalizability of topological rings, C. R. (Doklady) Acad. Sci. URSS. vol. 47 (1945) pp. 162-164. MR 14184
60.: M. Nagumo, Einige analytische Untersuchungen in linearen, metrischen Ringen, Jap. J. Math. vol. 13 (1936) pp. 61-80.
61.: A. Ostrowski, Über einige Lösungen der Funktionalgleichung $\psi(x)·\psi(x)=\psi(xy)$, Acta Math. vol. 41 (1918) pp. 271-284. MR 1555153
62.: Y. Otobe, On locally compact fields, Jap. J. Math. vol. 19 (1945) pp. 189-202. MR 14076
63.: F. Peter and H. Weyl, Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Math. Ann. vol. 97 (1927) pp. 737-755. MR 1512386
64.: L. Pontrjagin, Über stetige algebraische Körper, Ann. of Math. vol. 33 (1932) pp. 163-174. MR 1503043
65.: L. Pontrjagin, Topological groups, Princeton, 1939.
66.: D. Raikov, To the theory of normed rings with involution, C. R. (Doklady) Acad. Sci. URSS. vol. 54 (1946) pp. 387-390. MR 19845
67.: C. Rickart, Banach algebras with an adjoint operation, Ann. of Math. vol. 47 (1946) pp. 528-550. MR 17474
68.: C. Rickart, The singular elements of a Banach algebra, Duke Math. J. vol. 14 (1947) pp. 1063-1077. MR 23457
69.: I. Segal, The group algebra of a locally compact group, Trans. Amer. Math. Soc. vol. 61 (1947) pp. 69-105. MR 19617
70.: I. Segal, Irreducible representations of operator algebras, Bull. Amer. Math. Soc. vol. 53 (1947) pp. 73-88. MR 20217; 71 I. Segal, Postulates for general quantum mechanics, Ann. of Math. vol. 48 (1947) pp. 930-948. MR 22652
72.: I. Shafarevich, On the normalizability of topological fields, C. R. (Doklady) Acad. Sci. URSS. vol. 40 (1943) pp. 133-135. MR 11432
73.: G. Šilov, On the extension of maximal ideals, C. R. (Doklady) Acad. Sci. URSS. vol. 29 (1940) pp. 83-84. MR 4073
74.: G. Šilov, On regular normed rings, Travaux de l'institut mathématique Stekloff, Moscow, 1947.
75.: M. H. Stone, Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc. vol. 41 (1937) pp. 375-481. MR 1501905
76.: O. Taussky, Analytical methods in hypercomplex systems, Compositio Math. vol. 3 (1936) pp. 399-407. MR 1556953
77.: A. E. Taylor, The resolvent of a closed transformation, Bull. Amer. Math. Soc. vol. 44 (1938) pp. 70-74.
78.: A. E. Taylor, Analysis in complex Banach spaces, Bull. Amer. Math. Soc. vol. 49 (1943) pp. 652-669. MR 8644
79.: O. Teichmüller, Diskret bewertete perfekte Körper mit unvollkommenem Restklassenkörper, Journal für Mathematik vol. 176 (1937) pp. 141-152.
80.: A. Weil, L'intégration dans les groupes topologiques et ses applications, Actualités Scientifique et Industrielles, no. 869, Paris, 1938.
81.: K. Yosida, On the groups embedded in the metrical complete ring, Jap. J. Math. vol. 13 (1936) pp. 7-26.
82.: K. Yosida, Normed rings and spectral theorems I-VI, Proc. Imp. Acad. Tokyo vols. 19 and 20.
83.: D. Zelinsky, Topological characterization of fields with valuations, To appear in Bull Amer. Math. Soc. MR 28303

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