The power substitution for rings of complex and real functions on compact metric spaces
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- by A. N. Dranishnikov
- Proc. Amer. Math. Soc. 123 (1995), 2887-2893
- DOI: https://doi.org/10.1090/S0002-9939-1995-1307512-5
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Abstract:
The weak power substitution property for rings of matrices over the ring of functions on a compact metric space X is given in terms of cohomological dimension. A compactum with the ring of complex functions $C(X)$ having the following property is constructed: the units of $C(X)$ are not dense in $C(X)$ and they are dense among squares.References
- K. R. Goodearl, Power-cancellation of groups and modules, Pacific J. Math. 64 (1976), no. 2, 387–411. MR 450334, DOI 10.2140/pjm.1976.64.387
- K. R. Goodearl, Cancellation of low-rank vector bundles, Pacific J. Math. 113 (1984), no. 2, 289–302. MR 749537, DOI 10.2140/pjm.1984.113.289
- Rosa Camps and Pere Menal, The power substitution property for rings of continuous functions, J. Algebra 161 (1993), no. 2, 455–466. MR 1247366, DOI 10.1006/jabr.1993.1229
- V. I. Kuz′minov, Homological dimension theory, Uspehi Mat. Nauk 23 (1968), no. 5 (143), 3–49 (Russian). MR 0240813
- A. N. Dranishnikov, Homological dimension theory, Uspekhi Mat. Nauk 43 (1988), no. 4(262), 11–55, 255 (Russian); English transl., Russian Math. Surveys 43 (1988), no. 4, 11–63. MR 969565, DOI 10.1070/RM1988v043n04ABEH001900
- L. N. Vaseršteĭn, The stable range of rings and the dimension of topological spaces, Funkcional. Anal. i Priložen. 5 (1971), no. 2, 17–27 (Russian). MR 0284476
- A. N. Dranishnikov, Extension of mappings into CW-complexes, Mat. Sb. 182 (1991), no. 9, 1300–1310 (Russian); English transl., Math. USSR-Sb. 74 (1993), no. 1, 47–56. MR 1133570, DOI 10.1070/SM1993v074n01ABEH003333
- Albrecht Dold and René Thom, Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. (2) 67 (1958), 239–281 (German). MR 97062, DOI 10.2307/1970005
- Peter Hilton, Homotopy theory and duality, Gordon and Breach Science Publishers, New York-London-Paris, 1965. MR 0198466
- Dennis Sullivan, Geometric topology. Part I, Massachusetts Institute of Technology, Cambridge, Mass., 1971. Localization, periodicity, and Galois symmetry; Revised version. MR 0494074
- R. F. Williams, A useful functor and three famous examples in topology, Trans. Amer. Math. Soc. 106 (1963), 319–329. MR 146832, DOI 10.1090/S0002-9947-1963-0146832-0
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2887-2893
- MSC: Primary 55M10; Secondary 15A54, 16S60
- DOI: https://doi.org/10.1090/S0002-9939-1995-1307512-5
- MathSciNet review: 1307512