R Noetherian implies \(R\langle X\rangle\) is a Hilbert ring

DOI10.1016/0021-8693(80)90317-8zbMath0449.13002OpenAlexW2075596790MaRDI QIDQ1147190

James Brewer, William J. Heinzer

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0021-8693(80)90317-8

zbMATH Keywords

polynomial ringHilbert ringNoetherian ring

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative Noetherian rings and modules (13E05) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items (8)

The rings R(X) and \(R<X>\) ⋮ Semigroup rings ⋮ Prüfer conditions in the Nagata ring and the Serre’s conjecture ring ⋮ Krull and Global Dimensions of Semiprime Noetherian PI-Rings ⋮ Hereditary localization of polynomial rings ⋮ Maximal Ideals in Laurent Polynomial Rings ⋮ On treed Nagata rings ⋮ Two counterexamples about the Nagata and Serre conjecture rings

Cites Work

• The ring \(R<X>\)
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