Affine representations of $${ell}$$-groups and MV-algebras

Affine representations for archimedean ({ell})-groups and semisimple MV-algebras via embedding theorems are presented; they are simple to work with but powerful enough to express significant properties of our studied objects. Indeed, we focus on the space of particular homomorphisms between an archimedean ({ell})-group (a semisimple MV-algebra, respectively) and a vector lattice (a Riesz MV-algebra, respectively), i.e., the set of the generalized states, providing a general framework.