On lattice homomorphisms in Riesz spaces

TL;DR

This paper investigates the relationship between lattice and Riesz homomorphisms in Riesz spaces, establishing conditions under which lattice homomorphisms are also Riesz homomorphisms, extending previous theoretical results.

Contribution

It provides new conditions under which lattice homomorphisms in Riesz spaces are also Riesz homomorphisms, expanding the theoretical understanding of these structures.

Findings

Under certain conditions, lattice homomorphisms are Riesz homomorphisms.

Extends previous results by Mena, Roth, Thanh, Lochan, Strauss, Ercan, and Wickstead.

Connects lattice and Riesz homomorphisms in Riesz spaces.

Abstract

In this paper, we study the connextion between lattice and Riesz homomorphisms in Riesz spaces. We prove, under a certain condition, that any lattice homomorphism on Riesz space is a Riesz homomorphism. This fits in the type of results by Mena and Roth [7], thanh [9], Lochan and Strauss [5] and Ercan and Wickstead [2].