2007/10/01 by Jose Capco, Capco, Jose
Mathematics · #13B22 #13J25 (Primary) #16E50 (Secondary) #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #math.AG #msc:13B22 #msc:13J25 #msc:16E50
paper · pdf · doi:10.48550/arxiv.0710.0267
openalex publication_date 2007/10/01 · arxiv created 2007/12/12 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.