Uncountable 𝑛-dimensional excellent regular local rings with countable spectra

Uncountable $n$-dimensional excellent regular local rings with countable spectra
HTML articles powered by AMS MathViewer

by S. Loepp and A. Michaelsen PDF

Trans. Amer. Math. Soc. 373 (2020), 479-490 Request permission

We prove that, for any $n\geq 0$, there exists an uncountable $n$-dimensional excellent regular local ring with a countable spectrum.

References

Cory Colbert, Enlarging localized polynomial rings while preserving their prime ideal structure, J. Algebra (to appear).
Raymond C. Heitmann, Completions of local rings with an isolated singularity, J. Algebra 163 (1994), no. 2, 538–567. MR 1262718, DOI 10.1006/jabr.1994.1031
M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 43–60. MR 251026, DOI 10.1090/S0002-9947-1969-0251026-X
Hideyuki Matsumura, Commutative ring theory, 2nd ed., Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1989. Translated from the Japanese by M. Reid. MR 1011461
Christel Rotthaus, Excellent rings, Henselian rings, and the approximation property, Rocky Mountain J. Math. 27 (1997), no. 1, 317–334. MR 1453106, DOI 10.1216/rmjm/1181071964
Roger Wiegand and Sylvia Wiegand, Prime ideals in Noetherian rings: a survey, Ring and module theory, Trends Math., Birkhäuser/Springer Basel AG, Basel, 2010, pp. 175–193. MR 2744272, DOI 10.1007/978-3-0346-0007-1_{1}3
Weitao Zhu, An uncountable dimension-two ring with a countable spectrum, Undergraduate thesis, Williams College, advised by S. Loepp, 2018 (unpublished thesis).