Chinese Remainder Approximation Theorem

TL;DR

This paper generalizes the Chinese Remainder Theorem within topological rings, exploring ideal co-maximality, hyperspace uniformity, and interpolation theorems to extend classical results to more complex algebraic structures.

Contribution

It introduces a topological generalization of ideal co-maximality and proves a stronger version of the Chinese Remainder Theorem for infinite ideals in supercomplete, pseudo-valuated rings.

Findings

Generalized Chinese Remainder Theorem for topological rings

Proved stronger version for infinitely many ideals

Established two interpolation theorems

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.