We use the Fock semicrossed product to define an operator algebra associated to a module over an integral domain. We consider the $C^*$-envelope of the semicrossed product, and then consider properties of these algebras as models for studying general semicrossed products.
"Operator algebras associated to modules over an integral domain." Adv. Oper. Theory 3 (2) 374 - 387, Spring 2018. https://doi.org/10.15352/AOT.1706-1181