On the ideal structure of certain semirings and compactification of topological spaces
HTML articles powered by AMS MathViewer
- by J. G. Horne PDF
- Trans. Amer. Math. Soc. 90 (1959), 408-430 Request permission
References
- P. Alexandroff, Bikompakte Erweiterungen topologischer Räume, Rec. Math. [Mat. Sbornik] N.S. 5(47) (1939), 403–423 (Russian, with German summary). MR 0001914
- Richard F. Arens and Irving Kaplansky, Topological representation of algebras, Trans. Amer. Math. Soc. 63 (1948), 457–481. MR 25453, DOI 10.1090/S0002-9947-1948-0025453-6
- Garrett Birkhoff, Lattice Theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. 25, American Mathematical Society, New York, N. Y., 1948. MR 0029876
- Robert L. Blair, Stone’s topology for a binary relation, Duke Math. J. 22 (1955), 271–280. MR 70146
- Paul Civin and Bertram Yood, Ideals in multiplicative semi-groups of continuous functions, Duke Math. J. 23 (1956), 325–334. MR 78665
- Leonard Gillman and Melvin Henriksen, Concerning rings of continuous functions, Trans. Amer. Math. Soc. 77 (1954), 340–362. MR 63646, DOI 10.1090/S0002-9947-1954-0063646-5
- Melvin Henriksen, On the equivalence of the ring, lattice, and semigroup of continuous functions, Proc. Amer. Math. Soc. 7 (1956), 959–960. MR 82490, DOI 10.1090/S0002-9939-1956-0082490-3
- Edwin Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64 (1948), 45–99. MR 26239, DOI 10.1090/S0002-9947-1948-0026239-9
- N. Jacobson, A topology for the set of primitive ideals in an arbitrary ring, Proc. Nat. Acad. Sci. U.S.A. 31 (1945), 333–338. MR 13138, DOI 10.1073/pnas.31.10.333
- Irving Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617–623. MR 20715, DOI 10.1090/S0002-9904-1947-08856-X
- V. L. Klee Jr., Convex sets in linear spaces, Duke Math. J. 18 (1951), 443–466. MR 44014
- A. N. Milgram, Multiplicative semigroups of continuous functions, Duke Math. J. 16 (1949), 377–383. MR 29476 J. von Neumann, On regular rings, Proc. Nat. Acad. Sci. U.S.A. vol. 22 (1936) pp. 707-713.
- Georg Nöbeling, Grundlagen der analytischen Topologie, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXXII, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954 (German). MR 0068197
- Taira Shirota, A generalization of a theorem of I. Kaplansky, Osaka Math. J. 4 (1952), 121–132. MR 52760
- W. Słowikowski and W. Zawadowski, A generalization of maximal ideals method of Stone and Gelfand, Fund. Math. 42 (1955), 215–231. MR 80283, DOI 10.4064/fm-42-2-215-231
- M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375–481. MR 1501905, DOI 10.1090/S0002-9947-1937-1501905-7
- Henry Wallman, Lattices and topological spaces, Ann. of Math. (2) 39 (1938), no. 1, 112–126. MR 1503392, DOI 10.2307/1968717
Additional Information
- © Copyright 1959 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 90 (1959), 408-430
- MSC: Primary 46.00; Secondary 20.00
- DOI: https://doi.org/10.1090/S0002-9947-1959-0108714-9
- MathSciNet review: 0108714