On the Duality Principle for Linear Dynamical Systems Over Commutative Rings
نویسنده
چکیده
The main result in this paper characterizes those commutative rings R having the property that every linear dynamical system over R verifies the duality principle [i.e., the system 2 is observable (reachable) if and only if the dual system 8’ is reachable (observable)]. This characterization is given in terms of the finitely generated faithful ideals of R, and it generalizes a result due to Ching and Wyman for the noetherian case. In case R satisfies the additional condition of being a reduced ring, we prove that the duality principle holds in R if and only if the height of every finitely generated ideal of R is zero.
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