The conditions (𝐂ᵢ),𝐢=1,2,3,11,12, in rings, modules, categories, and lattices

DOI10.1090/conm/715/14401zbMath1441.06004OpenAlexW2892168884MaRDI QIDQ4961936

Toma L.Albu

Publication date: 29 October 2018

Published in: Advances in Rings and Modules (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/715/14401

zbMATH Keywords

modular latticeGrothendieck categorycontinuous latticecomplementCS moduleupper continuous latticecompact elementcompactly generated latticehereditary torsion theorypseudo-complementclosed elementessential elementlattice preradicallinear modular latticeCC lattice\((C_i)\) condition\(i=1,2,3, 11,12\)quasi-continuous latticethe Osofsky-Smith theorem

Mathematics Subject Classification ID

Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Abelian categories, Grothendieck categories (18E10) Other classes of modules and ideals in associative algebras (16D80) Continuous lattices and posets, applications (06B35) Modular lattices, Desarguesian lattices (06C05)

Cites Work

• New results on \(C_{11}\) and \(C_{12}\) lattices with applications to Grothendieck categories and torsion theories
• Lattice preradicals with applications to Grothendieck categories and torsion theories.
• On extending property on direct sums of uniform modules
• Cyclic modules whose quotients have all complement submodules direct summands
• Fully invariant-extending modular lattices, and applications. I.
• The conditions (C_i) in modular lattices, and applications
• Module Theory, Extending Modules and Generalizations
• The Osofsky–Smith Theorem for Modular Lattices and Applications (I)
• RINGS IN WHICH EVERY COMPLEMENT RIGHT IDEAL IS A DIRECT SUMMAND
• π-injective modules and rings whose cyclics are π-injective
• Localization of modular lattices, Krull dimension, and the Hopkins-Levitzki theorem (I)
• Generalizations of CS-modules
• The Osofsky-Smith Theorem for Modular Lattices, and Applications (II)
• A Torsion Theory for Abelian Categories
• On Continuous Rings and Self Injective Rings
• Des catégories abéliennes
• Modular C11 lattices and lattice preradicals
• On Regular Rings
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item