Amalgamation and extensions of summand absorbing modules over a semiring

TL;DR

This paper investigates the properties and behaviors of summand absorbing submodules over semirings, focusing on their amalgamation and extension, especially within the context of tropical algebra and upper bound modules.

Contribution

It introduces new theoretical insights into the structure and extension of summand absorbing modules over semirings, expanding understanding in tropical algebra.

Findings

Characterization of amalgamation properties of summand absorbing modules

Extension techniques for upper bound modules

Applications to tropical algebra structures

Abstract

A submodule $W$ of $V$ is summand absorbing, if $x + y \in W$ implies $x \in W, \; y \in W $ for any $x, y \in V$. Such submodules often appear in modules over (additively) idempotent semirings, particularly in tropical algebra. This paper studies amalgamation and extensions of these submodules, and more generally of upper bound modules.