SEMIGROUP C*-ALGEBRAS OF ax plus b-SEMIGROUPS

We study semigroup C*-algebras of ax+b-semigroups over integral domains. The goal is to generalize several results about C*-algebras of ax+b-semigroups over rings of algebraic integers. We prove results concerning K theory and structural properties like the ideal structure or pure infiniteness. Our methods allow us to treat ax+b-semigroups over a large class of integral domains containing all noetherian, integrally closed domains and coordinate rings of affine varieties over infinite fields.