# Multiplicative order convergence in $f$-algebras

## TL;DR

This paper introduces and studies the concept of multiplicative order convergence in $f$-algebras, defining related notions such as $mo$-convergence, $mo$-Cauchy, and $mo$-completeness, and explores their fundamental properties.

## Contribution

It presents new definitions and foundational properties of multiplicative order convergence in $f$-algebras, expanding the theoretical framework of order convergence.

## Key findings

- Defined $mo$-convergence, $mo$-Cauchy, and $mo$-complete in $f$-algebras
- Established basic properties of these notions
- Explored the structure of $mo$-KB-spaces

## Abstract

A net $(x_\alpha)$ in an $f$-algebra $E$ is said to be multiplicative order convergent to $x\in E$ if $\x_\alpha-x\u\oc 0$ for all $u\in E_+$. In this paper, we introduce the notions $mo$-convergence, $mo$-Cauchy, $mo$-complete, $mo$-continuous and $mo$-KB-space. Moreover, we study the basic properties of these notions.