Open AccessAlgebraic Structure of Linear Dynamical Systems. III. Realization Theory Over a Commutative Ring
Author(s) -
Yves Rouchaleau,
Bostwick F. Wyman,
R. E. Kalman
Publication year - 1972
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.69.11.3404
Subject(s) - realization (probability) , commutative ring , noetherian , commutative property , mathematics , ring (chemistry) , pure mathematics , finite field , algebraic number , class (philosophy) , field (mathematics) , integral domain , algebra over a field , domain (mathematical analysis) , principal (computer security) , dynamical systems theory , discrete mathematics , computer science , mathematical analysis , physics , quantum mechanics , statistics , chemistry , organic chemistry , artificial intelligence , operating system
The realization theory linear dynamical systems, previously developed over a field, are extended to a large class of commutative rings. The principal result is that the existence criterion for a finite realization extends without modification from a field to a Noetherian integral domain.