Chinese Remainder Approximation Theorem

2015/09/07 by Matan Komisarchik, Komisarchik, Matan
Mathematics · #13A18 #13J10 #30E05 #54E15 #54H13 #FOS: Mathematics #General Topology (math.GN) #Rings and Algebras (math.RA) #math.GN #math.RA #msc:13A18 #msc:13J10 #msc:30E05 #msc:54E15 #msc:54H13

paper · pdf · doi:10.48550/arxiv.1509.02188

22 pages

arxiv created 2016/07/02 · arxiv updated 2016/07/05

Abstract

We study a topological generalization of ideal co-maximality in topological rings and present some of its properties, including a generalization of the Chinese remainder theorem. Using the hyperspace uniformity, we prove a stronger version of this theorem concerning infinitely many ideals in supercomplete, pseudo-valuated rings. Finally we prove two interpolation theorems.

Related

• Interplay between the Chinese Remainder Theorem and the Lagrange Interpolation Formula
• Dao's question on the asymptotic behaviour of fullness
• Relative cofinality of ideals
• Formalization of Auslander--Buchsbaum--Serre criterion in Lean4
• Length, multiplicity, and multiplier ideals