On the duality principle for linear dynamical systems over commutative rings
| Autor: | Tomas Sanchez-Giralda, Jose A. Hermida-Alonso |
|---|---|
| Rok vydání: | 1990 |
| Předmět: |
Reduced ring
Discrete mathematics Noetherian Pure mathematics Numerical Analysis Algebra and Number Theory Mathematics::Commutative Algebra Zero (complex analysis) Observable Commutative ring Characterization (mathematics) Linear dynamical system Discrete Mathematics and Combinatorics Ideal (ring theory) Geometry and Topology Mathematics |
| Zdroj: | Linear Algebra and its Applications. 139:175-180 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/0024-3795(90)90397-u |
| Popis: | 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 Σ is observable (reachable) if and only if the dual system Σ t 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. |
| Databáze: | OpenAIRE |
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