Archimedean classes in additive monoids

Abstract

Summand absorbing submodules are common in modules over (additively) idempotent semirings, for example, in tropical algebra. A submodule [Formula: see text] of [Formula: see text] is summand absorbing, if [Formula: see text] implies [Formula: see text] for any [Formula: see text]. This paper proceeds the study of these submodules, and more generally of additive monoids, with emphasis on their archimedean classes and quotient structures.