Ore localisation for differential graded rings; towards Goldie's theorem for differential graded algebras

We study Ore localisation of differential graded algebras. Further we define dg-prime rings, dg-semiprime rings, and study the dg-nil radical of dg-rings. Then, we define dg-essential submodules, dg-uniform dimension, and apply all this to a dg-version of Goldie's theorem on prime dg-rings.

Saved in:
Bibliographic Details
Published inJournal of algebra Vol. 663; pp. 48 - 80
Main Author Zimmermann, Alexander
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2025
Elsevier
Subjects
Differential graded algebras
Goldie's theorem
Mathematics
Ore localisation
secondary
Differential graded algebras
Goldie's theorem
primary
Ore localisation
16W50
differential graded algebras
Mathematics Subject Classification. Primary: 16E45
Secondary: 16N40
16N60
Online AccessGet full text
ISSN0021-8693
1090-266X
DOI10.1016/j.jalgebra.2024.08.032

Cover

More Information
Summary:We study Ore localisation of differential graded algebras. Further we define dg-prime rings, dg-semiprime rings, and study the dg-nil radical of dg-rings. Then, we define dg-essential submodules, dg-uniform dimension, and apply all this to a dg-version of Goldie's theorem on prime dg-rings.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2024.08.032