2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69822A behavior is a closed shift invariant subspace of the space of sequences with entries in a field k. We work out an explicit duality for k-modules. This duality is then used to derive properties of behaviors, and their high dimensional and noncommutative generalizations.19 pages, minor changesOptimization and ControlRings and AlgebrasPrimary: 93C05; Secondary: 93B25, 16W80, 13J10, 16P40text