Pole assignability in polynomial rings, power series rings, and Prüfer domains. (English) Zbl 0611.13016
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.
Reviewer: W.Heinzer
MSC:
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
| 13F05 | Dedekind, Prüfer, Krull and Mori rings and their generalizations |
| 13F25 | Formal power series rings |
| 13A99 | General commutative ring theory |
Keywords:
polynomial ring; simultaneous basis property; algebraic systems theory; pole assignability; power series rings; Prüfer domains; Bezout domainReferences:
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