Amalgamation and extensions of summand absorbing modules over a semiring

Abstract

A submodule W of V is summand absorbing, if x+y ∈ W implies x ∈ W, y ∈ W for any x, y ∈ 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.