Pole assignability in polynomial rings, power series rings, and Prüfer domains
The authors mention that the topics treated in this paper have their origins in algebraic systems theory but that the paper itself should be classified as pure commutative algebra. If a system (F,G) over a commutative ring R is pole assignable, then it is known that the system is reachable in the sense that the R-module generated by the columns of \([G,FG,...,F^{n-1}G]\) is \(R^ n\). This paper is concerned with determining those rings for which the converse is true. Several properties related to pole assignability are also studied, especially for the case of polynomial or power series rings. A question concerning Prüfer domains is raised that is similar to the open question of whether every Bezout domain is an elementary divisor domain.
scientific article; zbMATH DE number 3987424
scientific article