OU-OSU Ring Theory Seminar
Cardinalities of Residue Fields of Noetherian Integral Domains, by Greg Oman (Ohio University)
| What |
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|---|---|
| When |
Oct 09, 2009 from 04:45 pm to 06:00 pm |
| Where | MW 154 (Columbus campus of Ohio State University) |
| Contact Name | Sergio Lopez |
| Contact Email | lopez@math.ohiou.edu |
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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 ZFC that there is a Noetherian domain of cardinality aleph 1 with a finite residue field, but the statement "There is a Noetherian domain of size aleph 2 with a finite residue field" is equivalent to the negation of the Continuum Hypothesis. If time permits, applications will be provided (characterizing the ordered set Spec(R[x]) when R is one-dimensional and semi-local). This is joint work with Keith Kearnes of The University of Colorado. The logic/set theory employed is not advanced and will be very accessible to non-specialists.
Note: This event takes place in Columbus Ohio.
