On Homogeneous Prime Spectra of Certain Rees Rings

DOI10.1080/00927870802255311zbMath1177.13011OpenAlexW2033879971MaRDI QIDQ3619840

David E. Rush, Louis J. jun. Ratliff

Publication date: 9 April 2009

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

Full work available at URL: https://doi.org/10.1080/00927870802255311

zbMATH Keywords

filtrationprime ideallocal ringgraded ringRees ringintegrally closed idealprojectively equivalent idealsform ringgoing downextended Rees ringgoing upessentially powers filtrationfiber ringprojectively full idealsrestricted Rees ring

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Ideals and multiplicative ideal theory in commutative rings (13A15) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items

Prereductions of ideals in local rings ⋮ Projectively full radical ideals in integral extension rings

Cites Work

• Projectively full ideals in noetherian rings
• Projectively full ideals in noetherian rings. II.
• Rees valuations and asymptotic primes of rational powers in noetherian rings and lattices
• Notes on essentially powers filtrations
• Hilbert coefficients of Hilbert filtrations
• Projectively equivalent ideals and Rees valuations
• Projectively full radical ideals in integral extension rings
• Some asymptotic properties of powers of ideals
• The $a$-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings
• Valuations Associated with Ideals (II)
• A note on form rings and ideals
• Form rings and projective equivalence
• The Geometry of Schemes
• Reduction number and a-Invariant of good filtrations
• Postulation number of good filtrations
• Analytic spread of nitrations, asymptotic nature and some stability properties
• Depth formulas for the rees algebras of filtrations
• Characterizations of Catenary Rings