Pole assignability in polynomial rings, power series rings, and Prüfer domains
type: Item
instance of: scholarly article
title: Pole assignability in polynomial rings, power series rings, and Prüfer domains
zbMATH Open document ID: 0611.13016
DOI: 10.1016/0021-8693(87)90031-7
author: James Brewer
author: Daniel Katz
author: W. Ullery
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13F25
Mathematics Subject Classification ID: 13A99
zbMATH DE Number: 3987424
zbMATH Keywords: polynomial ring
zbMATH Keywords: simultaneous basis property
zbMATH Keywords: algebraic systems theory
zbMATH Keywords: pole assignability
zbMATH Keywords: power series rings
zbMATH Keywords: Prüfer domains
zbMATH Keywords: Bezout domain
reviewed by: William J. Heinzer
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90031-7
OpenAlex ID: W1965424606
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description: scientific article; zbMATH DE number 3987424