A boundary quotient diagram for right LCM semigroups

We propose a boundary quotient diagram for right LCM semigroups with property (AR) that generalizes the boundary quotient diagram for N⋊N×. Our approach focuses on two important subsemigroups: the core subsemigroup and the semigroup of core irreducible elements. The diagram is then employed to unify several case studies on KMS-states, and we end with a discussion on K-theoretical aspects of the diagram motivated by recent findings for integral dynamics. This research has been published in Semigroup Forum. © 2017 Springer Verla