Uniqueness of real closure * of Baer regular rings
Abstract
It was pointed out in my last paper that there are rings whose real closure * are not unique. In [4] we also discussed some example of rings by which there is a unique real closure * (mainly the real closed rings). Now we want to determine more classes of rings by which real closure * is unique. The main results involve characterisations of domains and Baer regular rings having unique real closure *, and an example showing that regular rings need not be f-rings in order to have a unique real closure *. The main objective here is to find characterisation for uniqueness of real closure * for real regular rings that will primarily only require information of the prime spectrum and the real spectrum of the ring.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2007
- DOI:
- 10.48550/arXiv.0710.0267
- arXiv:
- arXiv:0710.0267
- Bibcode:
- 2007arXiv0710.0267C
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- 13J25 (Primary);
- 13B22;
- 16E50 (Secondary)