Decomposition of modules over generalized Dickson algebras

The article is devoted to modules over generalized Dickson algebras. These algebras are nonassociative and generally can be nonalternative. They compose an important class of algebras and an area in mathematics. Left, right and two-sided modules over generalized Dickson algebras are studied. Their structure and submodules are investigated. Bimodules with involution are scrutinized over generalized Dickson algebras with involution. Such bimodules have specific features caused by involution. Minimal submodules and decomposition of modules are investigated. In particular, cyclic submodules are studied.