An Open Mapping Theorem for rings which have a zero sequence of units

TL;DR

This paper establishes an Open Mapping Theorem for topological modules over rings with a zero sequence of units, and demonstrates the uniqueness of certain topologies on finitely generated modules over specific topological rings.

Contribution

It introduces an Open Mapping Theorem for modules over rings with a zero sequence of units and characterizes unique topologies on finitely generated modules over certain topological rings.

Findings

Open Mapping Theorem for modules over rings with zero units sequence

Unique complete, metrisable topology on finitely generated modules over specific rings

Application to Tate rings and related structures

Abstract

This paper provides an Open Mapping Theorem for topological modules over rings that have a zero sequence consisting of units. As an application it is shown that there is a unique complete and metrisable topology on finitely generated modules over certain topological rings (e.g. over complete noetherian Hausdorff Tate rings).