Startseite Mathematik Z r -graded rings and their canonical modules
Kapitel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Z r -graded rings and their canonical modules

  • Margherita Barile und Winfried Bruns
Veröffentlichen auch Sie bei De Gruyter Brill
Erkunden Sie dieses Fachgebiet So veröffentlichen Sie bei uns
Commutative Algebra
Ein Kapitel aus dem Buch Commutative Algebra

Abstract

In “Cohen–Macaulay rings” Bruns and Herzog define the graded canonical module for Z -graded rings. We generalize the definition to multigradings and prove that the canonical module “localizes.” As an application, we give a divisorial proof of the theorem of Danilov and Stanley on the canonical module of affine normal monoid rings. Along the way, we develop the basic theory of multigraded rings and modules.

Abstract

In “Cohen–Macaulay rings” Bruns and Herzog define the graded canonical module for Z -graded rings. We generalize the definition to multigradings and prove that the canonical module “localizes.” As an application, we give a divisorial proof of the theorem of Danilov and Stanley on the canonical module of affine normal monoid rings. Along the way, we develop the basic theory of multigraded rings and modules.

Kapitel in diesem Buch

  1. Frontmatter I
  2. Preface V
  3. Contents VII
  4. Wolmer Vasconcelos, a tribute IX
  5. Vasconcelos Bibliography (1964–2024) XVII
  6. The early years: flatness, projectivity, and R-sequences 1
  7. Joint work with Wolmer Vasconcelos. The early years 41
  8. Homological properties of the module of differentials 71
  9. Hilbert coefficients and Sally modules: a survey of Vasconcelos’ contributions 97
  10. Graph rings and ideals: Wolmer Vasconcelos’ contributions 133
  11. Degrees: Vasconcelos contributions 203
  12. The books of Wolmer V. Vasconcelos 241
  13. Finding nilpotents with Wolmer Vasconcelos 261
  14. Rees algebras over residual intersections 279
  15. Structure theorems for Gorenstein ideals of codimension four with small number of generators 297
  16. Sifted degrees of the equations of the Rees module and their connection with the Artin–Rees numbers 333
  17. Reembeddings of special border basis schemes 353
  18. Z r -graded rings and their canonical modules 389
  19. Rings with q-torsionfree canonical modules 405
https://doi.org/10.1515/9783110999365-013

Kapitel in diesem Buch

  1. Frontmatter I
  2. Preface V
  3. Contents VII
  4. Wolmer Vasconcelos, a tribute IX
  5. Vasconcelos Bibliography (1964–2024) XVII
  6. The early years: flatness, projectivity, and R-sequences 1
  7. Joint work with Wolmer Vasconcelos. The early years 41
  8. Homological properties of the module of differentials 71
  9. Hilbert coefficients and Sally modules: a survey of Vasconcelos’ contributions 97
  10. Graph rings and ideals: Wolmer Vasconcelos’ contributions 133
  11. Degrees: Vasconcelos contributions 203
  12. The books of Wolmer V. Vasconcelos 241
  13. Finding nilpotents with Wolmer Vasconcelos 261
  14. Rees algebras over residual intersections 279
  15. Structure theorems for Gorenstein ideals of codimension four with small number of generators 297
  16. Sifted degrees of the equations of the Rees module and their connection with the Artin–Rees numbers 333
  17. Reembeddings of special border basis schemes 353
  18. Z r -graded rings and their canonical modules 389
  19. Rings with q-torsionfree canonical modules 405
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 8.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/9783110999365-013/html
Button zum nach oben scrollen