Elementary extensions of linear topological abelian groups
HTML articles powered by AMS MathViewer
- by R. G. Phillips and P. L. Sperry PDF
- Proc. Amer. Math. Soc. 31 (1972), 525-528 Request permission
Abstract:
R. MacDowell and E. Specker obtain a structure theorem for elementary extensions of the integers by considering a certain residue mapping. In this paper we characterize those abelian groups in which an analogous situation exists and obtain the MacDowell-Specker result as a special case of our theory.References
- N. Bourbaki, Éléments de mathématique. Première partie. (Fascicule III.) Livre III; Topologie générale. Chap. 3: Groupes topologiques. Chap. 4: Nombres réels, Hermann, Paris, 1960 (French). Troisième édition revue et augmentée; Actualités Sci. Indust., No. 1143. MR 0140603
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
- R. Mac Dowell and E. Specker, Modelle der Arithmetik, Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Pergamon, Oxford; Państwowe Wydawnictwo Naukowe, Warsaw, 1961, pp. 257–263 (German). MR 0152447
- Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854
- Joseph Rotman, A completion functor on modules and algebras, J. Algebra 9 (1968), 369–387. MR 229684, DOI 10.1016/0021-8693(68)90009-4
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 525-528
- DOI: https://doi.org/10.1090/S0002-9939-1972-0288212-4
- MathSciNet review: 0288212