Pole assignability and the invariant factor theorem in Prüfer domains and Dedekind domains

DOI10.1016/0021-8693(87)90236-5zbMath0659.13004OpenAlexW2054224662MaRDI QIDQ1112117

Lee Klingler, James Brewer

Publication date: 1987

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90236-5

zbMATH Keywords

Dedekind domainsPrüfer domainsGCU-propertypole assignability propertytorsion free Picard group

Mathematics Subject Classification ID

Pole and zero placement problems (93B55) Algebraic methods (93B25) Polynomials over commutative rings (13B25) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (14)

\(\mathbb{C}[y\) is a CA-ring and coefficient assignment is properly weaker than feedback cyclization over a PID] ⋮ Pole shifting for families of systems: The dimension one case ⋮ Dynamic feedback over commutative rings ⋮ Does Int \((\mathbb Z)\) have the stacked bases property? ⋮ The ring of integer-valued polynomials of a semi-local principal-ideal domain ⋮ Feedback cyclization for rings with finite stable range ⋮ Strong feedback cyclization for systems over rings ⋮ Dynamic feedback over rings whose homomorphic images are local-global ⋮ Finitely Presented Modules Over Semihereditary Rings ⋮ Prüfer domains of integer-valued polynomials and the two-generator property ⋮ Block diagonalization and $2$-unit sums of matrices over Prüfer domains ⋮ Idempotent Pairs and PRINC Domains ⋮ Locally isomorphic torsionless modules over domains of finite character ⋮ Integer-valued polynomials, Prüfer domains and the stacked bases property

Cites Work

• Unnamed Item
• Invariant factor theorem for Prüfer domains of finite character
• Pole assignment for systems over rings
• The pole assignability property in polynomial rings over GCD-domains
• Pole assignability in polynomial rings, power series rings, and Prüfer domains
• On the pole assignability property over commutative rings
• New results on pole-shifting for parametrized families of systems
• On \(\text{Pic}(R[X)\) for \(R\) seminormal]
• Remarks on the pole-shifting problem over rings
• Module equivalences: Local to global. When primitive polynomials represent units
• 1 1/2 and 2 generator ideals in Prüfer domains
• On the number of generators of an invertible ideal
• Projective Modules Over Rings with Many Units
• Modules Over Dedekind Rings and Valuation Rings

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