Uniqueness of real closure * of Baer regular rings
Commutative Algebra
2015-03-13 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.0710.0267,
title = {Uniqueness of real closure * of Baer regular rings},
author = {Jose Capco},
journal= {arXiv preprint arXiv:0710.0267},
year = {2015}
}