Cardinalities of Residue Fields of Noetherian Integral Domains |
| |
| Authors: | Keith A Kearnes Greg Oman |
| |
| Institution: | 1. Department of Mathematics , University of Colorado , Boulder, Colorado, USA kearnes@euclid.colorado.edu;3. Department of Mathematical Sciences , Otterbein College , Westerville, Ohio, USA |
| |
| Abstract: | We determine the relationship between the cardinality of a Noetherian integral domain and the cardinality of a residue field. One consequence of the main result is that it is provable in Zermelo–Fraenkel Set Theory with Choice (ZFC) that there is a Noetherian domain of cardinality ?1 with a finite residue field, but the statement “There is a Noetherian domain of cardinality ?2 with a finite residue field” is equivalent to the negation of the Continuum Hypothesis. |
| |
| Keywords: | Generalized continuum hypothesis Integral domain Noetherian ring Prime spectrum Residue field |
|
|
