Lattice preradicals with applications to Grothendieck categories and torsion theories.

DOI10.1016/j.jalgebra.2015.07.030zbMath1327.06009OpenAlexW1917447294WikidataQ116296819 ScholiaQ116296819MaRDI QIDQ745166

Mihai Iosif, Toma L.Albu

Publication date: 13 October 2015

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2015.07.030

zbMATH Keywords

complete latticestracemodular latticesJacobson radicalsoclesradicalsatomspreradicalscoatomscompactly generated latticeslinear modular latticesrejectupper continuous lattices

Mathematics Subject Classification ID

Complete lattices, completions (06B23) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Continuous lattices and posets, applications (06B35) Modular lattices, Desarguesian lattices (06C05)

Related Items (18)

Goldie extending property on the class of exact submodules ⋮ New results on \(C_{11}\) and \(C_{12}\) lattices with applications to Grothendieck categories and torsion theories ⋮ Strongly fully invariant-extending modular lattices ⋮ Prime, irreducible, and completely irreducible lattice preradicals on modular complete lattices (I) ⋮ Relativization, absolutization, and latticization in ring and module theory ⋮ Weak Rickart and dual weak Rickart objects in abelian categories ⋮ On the lattice of conatural classes of linear modular lattices ⋮ On torsion theories and open classes of linear modular lattices ⋮ Some isomorphic big lattices and some properties of lattice preradicals ⋮ Big lattices of hereditary and natural classes of linear modular lattices ⋮ Fully invariant-extending modular lattices, and applications. I. ⋮ Modular C11 lattices and lattice preradicals ⋮ The conditions (𝐂ᵢ),𝐢=1,2,3,11,12, in rings, modules, categories, and lattices ⋮ Singular and nonsingular modules relative to a torsion theory ⋮ Comultiplication modules relative to a hereditary torsion theory ⋮ When some complement of an exact submodule is a direct summand ⋮ Modules whose exact submodules are essentially embedded in summands ⋮ Extending properties of exact projection invariant submodules

Cites Work

• The kernels of completion maps and a relative form of Nakayama's lemma
• The descending chain condition relative to a torsion theory
• The conditions (C_i) in modular lattices, and applications
• Localization of modular lattices, krull dimension, and the hopkins-levitzki theorem (II)
• Localization of modular lattices, Krull dimension, and the Hopkins-Levitzki theorem (I)
• The Osofsky-Smith Theorem for Modular Lattices, and Applications (II)
• Modular C11 lattices and lattice preradicals
• 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

This page was built for publication: Lattice preradicals with applications to Grothendieck categories and torsion theories.