Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401Operator algebras associated to modules over an integral domain3743875111910.15352/aot.1706-1181ENBenton DuncanDepartment of Mathematics, North Dakota State University, Fargo, North Dakota, USAJournal Article20170615We 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.http://www.aot-math.org/article_51119_929777a0cb213c0b5b50c5e587f49eb8.pdf