Archimedean classes in additive monoids

Abstract

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 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. This paper proceeds the study of these submodules, and more generally of additive monoids, with emphasis on their archimedean classes and quotient structures.