  Summand absorbing submodules are common in modules over (additively)
idempotent semirings, for example, in tropical algebra. A submodule $W$ of $V$
is summand absorbing, if $x + y \in W$ implies $x \in W, \; y \in W $ for any
$x, y \in V$. This paper proceeds the study of these submodules, and more
generally of additive monoids, with emphasis on their archimedean classes and
quotient structures.
