Two criteria for locally Noetherian Grothendieck categories

DOI10.1016/J.JPAA.2022.107233OpenAlexW4293833177MaRDI QIDQ2079659

Yanyan Li

Publication date: 30 September 2022

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2022.107233

zbMATH Keywords

Grothendieck categorieschain conditionsfinitely injective objectslocal summands

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Module categories in associative algebras (16D90) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Projectives and injectives (category-theoretic aspects) (18G05) Abelian categories, Grothendieck categories (18E10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some remarks on a theorem of Bergman
• Flat endofinite modules, prime ideals, and duality.
• On the existence of non-trivial finitely injective modules.
• Rings whose modules have maximal or minimal injectivity domains.
• Injective modules over Noetherian rings
• Some decomposition properties of injective and pure-injective modules
• Indecomposable decompositions of finitely presented pure-injective modules
• Nonsingular CS-rings coincide with tight PP rings.
• \(\Sigma\)-extending modules
• A generalization of the Mitchell lemma: the Ulmer theorem and the Gabriel-Popescu theorem revisited
• Classes of almost clean rings.
• Rings whose pure-injective right modules are direct sums of lifting modules.
• Every Σ-CS-module has an indecomposable decomposition
• Ziegler's Indecomposability Criterion
• The Structure of Prime Rings Under Ascending Chain Conditions
• Semi-Prime Rings with Maximum Condition
• On the Sparsity of Representations of Rings of Pure Global Dimension Zero
• Rings whose modules are direct sums of extending modules
• Duality and Pure-Semisimple Rings
• On finitely injective modules and locally pure-injective modules over Prüfer domains
• Categories and Sheaves
• On Continuous Rings and Self Injective Rings
• Rings with Ascending Condition on Annihilators
• On finitely injective modules
• On the Decomposition of Nonsingular CS-Modules
• Continuous Geometry
• Indecomposable decompositions of pure-injective objects and the pure-semisimplicity.

This page was built for publication: Two criteria for locally Noetherian Grothendieck categories