Approximating PA

Wiid, F. G. J.

doi:10.1090/S0002-9939-1988-0955007-7

Approximating PA
HTML articles powered by AMS MathViewer

by F. G. J. Wiid PDF

Proc. Amer. Math. Soc. 103 (1988), 1192-1195 Request permission

Abstract:

It is shown that the ring of continuous real-valued functions on a compact Hausdorff space of dimension $\leq 1$ is a BCS-ring. This result follows from a study of the preservation of the PA and BCS properties under certain ring-theoretic constructions.

References

James Brewer, Daniel Katz, and William Ullery, Pole assignability in polynomial rings, power series rings, and Prüfer domains, J. Algebra 106 (1987), no. 1, 265–286. MR 878478, DOI 10.1016/0021-8693(87)90031-7
M. L. J. Hautus and Eduardo D. Sontag, New results on pole-shifting for parametrized families of systems, J. Pure Appl. Algebra 40 (1986), no. 3, 229–244. MR 836650, DOI 10.1016/0022-4049(86)90043-5
Sibe Mardešić, On covering dimension and inverse limits of compact spaces, Illinois J. Math. 4 (1960), 278–291. MR 116306
F. Minnaar, C. G. Naudé, G. Naudé, and F. Wiid, Pole assignability of rings of low dimension, J. Pure Appl. Algebra 51 (1988), no. 1-2, 197–203. MR 941901, DOI 10.1016/0022-4049(88)90089-8
Richard G. Swan, Topological examples of projective modules, Trans. Amer. Math. Soc. 230 (1977), 201–234. MR 448350, DOI 10.1090/S0002-9947-1977-0448350-9
W. V. Vasconcelos and C. A. Weibel, bcs rings, J. Pure Appl. Algebra 52 (1988), no. 1-2, 173–185. MR 949348, DOI 10.1016/0022-4049(88)90145-4
F. G. J. Wiid, Noetherian rings of dimension one are pole assignable, J. Pure Appl. Algebra 53 (1988), no. 1-2, 197–199. MR 955618, DOI 10.1016/0022-4049(88)90020-5