The ring \(R<X>\)

DOI10.1016/0021-8693(80)90164-7zbMath0461.13008OpenAlexW2161999858MaRDI QIDQ1152417

L. R. le Riche

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)90164-7

zbMATH Keywords

\(R<X>\)localization at monic polynomials

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Principal ideal rings (13F10) Polynomials over commutative rings (13B25) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (19)

A question about saturated chains of primes in Serre conjecture rings ⋮ The rings R(X) and \(R<X>\) ⋮ Semigroup rings ⋮ Prüfer conditions in the Nagata ring and the Serre’s conjecture ring ⋮ ALMOST MULTIPLICATIVE SETS ⋮ Noether normalization theorem and dynamical Gröbner bases over Bézout domains of Krull dimension 1 ⋮ R Noetherian implies \(R\langle X\rangle\) is a Hilbert ring ⋮ Trace properties and the rings \(R(x)\) and \(R\langle x\rangle\) ⋮ \(t\)-splitting sets in integral domains. ⋮ Krull and Global Dimensions of Semiprime Noetherian PI-Rings ⋮ Hereditary localization of polynomial rings ⋮ Endomorphism rings, power series rings, and serial modules ⋮ Unnamed Item ⋮ THE S-FINITENESS ON QUOTIENT RINGS OF A POLYNOMIAL RING ⋮ On treed Nagata rings ⋮ Cleanness of overrings of polynomial rings ⋮ Gaussian Property of the RingsR(X) andR〈X〉 ⋮ Semidistributive modules ⋮ Distributive semigroup rings and related topics

Cites Work

• On semi-hereditary rings
• Serre's conjecture
• Overrings of Commutative Rings. II. Integrally Closed Overrings
• Kronecker Function Rings and Flat D[ X -Modules]
• Sur la compacité du spectre minimal d'un anneau
• Projective modules over polynomial rings
• Projective modules over some non-noetherian polynomial rings
• Prüfer rings
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