The conditions (Ci) in modular lattices, and applications

DOI10.1142/S0219498816500018zbMath1367.06002MaRDI QIDQ2788746

Mihai Iosif, Adnan Tercan, Toma L.Albu

Publication date: 22 February 2016

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

Grothendieck categorytorsion theorypseudo-complementCS-moduleupper continuous modular lattice

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Continuous lattices and posets, applications (06B35) Modular lattices, Desarguesian lattices (06C05)

Related Items (10)

New results on \(C_{11}\) and \(C_{12}\) lattices with applications to Grothendieck categories and torsion theories ⋮ Strongly fully invariant-extending modular lattices ⋮ Relativization, absolutization, and latticization in ring and module theory ⋮ 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 ⋮ Lattice preradicals with applications to Grothendieck categories and torsion theories. ⋮ 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

• Cyclic modules whose quotients have all complement submodules direct summands
• The Osofsky–Smith Theorem for Modular Lattices and Applications (I)
• Generalizations of CS-modules
• The Osofsky-Smith Theorem for Modular Lattices, and Applications (II)
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