Lattice structure on bounded homomorphisms between topological lattice rings

TL;DR

This paper investigates the lattice structure of bounded homomorphisms on locally solid lattice rings, demonstrating that under certain conditions, these homomorphisms form locally solid lattice rings.

Contribution

It introduces a lattice structure on bounded homomorphisms of locally solid lattice rings, showing they form locally solid lattice rings under mild assumptions.

Findings

Bounded homomorphisms form locally solid lattice rings.

Lattice structures are established under mild conditions.

The work extends the understanding of topological ring homomorphisms.

Abstract

Suppose $X$ is a locally solid lattice ring. It is known that there are three classes of bounded group homomorphisms on $X$ whose topological structures make them again topological rings. In this note, we consider lattice structure on them; more precisely, we show that, under some mild assumptions, they are locally solid lattice rings.