Originalversjon
Journal of Mathematical Analysis and Applications. 2016, 438 (2), 772-789, DOI: http://dx.doi.org/10.1016/j.jmaa.2016.02.015
Sammendrag
We introduce the notion of accurate foundation sets and the accurate refinement property for right LCM semigroups. For right LCM semigroups with this property, we derive a more explicit presentation of the boundary quotient. In the context of algebraic dynamical systems, we also analyse finiteness properties of foundation sets which lead us to a very concrete presentation. Based on Starling's recent work, we provide sharp conditions on certain algebraic dynamical systems for pure infiniteness and simplicity of their boundary quotient.