Split objects with respect to a fully invariant short exact sequence in abelian categories

DOI10.4171/RSMUP/88zbMath1497.18009arXiv1803.05060OpenAlexW4225674180MaRDI QIDQ2154567

Septimiu Crivei, Derya Keskin Tütüncü, Rachid Tribak

Publication date: 20 July 2022

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.05060

zbMATH Keywords

abelian category(dual) (strongly) \(F\)-split object(dual) (strongly) Rickart objectfully invariant short exact sequence

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Abelian categories, Grothendieck categories (18E10)

Related Items (2)

CS-Baer and dual CS-Baer objects in abelian categories ⋮ Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Direct sums of Rickart modules.
• The splitting problem for coalgebras.
• Relative regular objects in categories.
• Rickart and dual Rickart objects in abelian categories: transfer via functors
• Strongly lifting modules and strongly dual Rickart modules
• Rickart and dual Rickart objects in abelian categories
• T-dual Rickart modules
• Banach algebras with an adjoint operation
• Modules in Which Inverse Images of Some Submodules are Direct Summands
• Dual Rickart Modules
• T-Rickart modules
• A dual approach to the theory of inverse split modules
• Direct Products of Modules
• DUO MODULES
• t-Rickart and Dual t-Rickart Modules
• Covers in finitely accessible categories
• ON DUAL BAER MODULES
• V-Categories: Applications to Graded Rings
• Properties of direct summands of modules
• Baer and Quasi-Baer Modules
• Generalizations of the Simple Torsion Class and the Splitting Properties
• All finitely generatedM-subgenerated modules are extending
• Hereditary coalgebras
• Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories
• Strongly Rickart objects in abelian categories
• Strongly Rickart objects in abelian categories: Applications to strongly regular and strongly Baer objects
• Rickart Modules
• Flat Comodules and Perfect Coalgebras
• Monomorphisms, Epimorphisms, and Pull-Backs
• A Foundation of Torsion Theory for Modules Over General Rings
• Modules Over Dedekind Rings and Valuation Rings
• Modules with the summand intersection property

This page was built for publication: Split objects with respect to a fully invariant short exact sequence in abelian categories