Abstract

In the present note we prove a representation theorem for primely generated regular refinement monoids in terms of partially ordered systems of commutative groups. This gives, in particular, a classification of all finite refinement monoids. Throughout, all monoids and groups are commutative. Let M= (M; +, 0) be a monoid. M is called a refinement monoid [2-5, 81 if the following conditions are satisfied:

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