Classification of split torsion torsionfree triples in module categories.

DOI10.1016/j.jpaa.2006.04.003zbMath1121.16027arXivmath/0511159OpenAlexW2056916868MaRDI QIDQ860431

Pedro Nicolás, Manuel Saorín

Publication date: 9 January 2007

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

Full work available at URL: https://arxiv.org/abs/math/0511159

zbMATH Keywords

torsion theoriescategories of modulescentrally split TTF-triplesleft-split TTF-triplesright-split TTF-triples

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Torsion theories, radicals (18E40) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) General module theory in associative algebras (16D10)

Related Items (8)

Lattice decomposition of modules over commutative rings ⋮ Relation between balanced pairs and TTF triples ⋮ Partial silting objects and smashing subcategories ⋮ Generalized tilting theory ⋮ Lifting and restricting recollement data ⋮ Torsion pairs in categories of modules over a preadditive category ⋮ Recollements of module categories ⋮ A representation-theoretic approach to recollements of abelian categories

Cites Work

• Tame algebras and integral quadratic forms
• Some aspects of torsion
• Homological dimension and splitting torsion theories
• Direct Products of Modules
• Splitting torsion theories
• Tilted Algebras
• PURE AND FINITELY PRESENTABLE MODULES, DUALITY HOMOMORPHISMS AND THE COHERENCE PROPERTY OF A RING
• ABELIAN EXACT SUBCATEGORIES CLOSED UNDER PREDECESSORS
• Tilting in abelian categories and quasitilted algebras
• Semihereditary rings
• Singular torsion and the splitting properties
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