Amalgamation and extensions of summand absorbing modules over a semiring

Abstract

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