Cotorsion theories and splitters

DOI10.1090/S0002-9947-00-02475-2zbMath0962.20039arXivmath/9910159OpenAlexW2102125707MaRDI QIDQ4505924

Saharon Shelah, Rüdiger Göbel

Publication date: 3 October 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9910159

zbMATH Keywords

completionscotorsion theoriessplittersenough injectivesself-splitting modulesAbelian extensions of Abelian groupsenough projectivesrealising rings as endomorphism rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Model-theoretic algebra (03C60) Projective and free modules and ideals in commutative rings (13C10) Projectives and injectives (category-theoretic aspects) (18G05) Extensions of abelian groups (20K35) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Homological and categorical methods for abelian groups (20K40) Injective and flat modules and ideals in commutative rings (13C11)

Related Items

On the cogeneration of cotorsion pairs ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the Pure-injectivity Profile of a Ring ⋮ Baer cotorsion pairs. ⋮ Remarks about the history of Abelian groups in England and Germany. ⋮ Extensions in the class of countable torsion-free Abelian groups. ⋮ Cotilting and a hierarchy of almost cotorsion groups ⋮ Self-splitting Abelian groups ⋮ Large indecomposable roots of Ext ⋮ On the lattice of cotorsion theories ⋮ Envelopes and covers by modules of finite injective and projective dimensions ⋮ Flat covers and cotorsion envelopes of sheaves ⋮ An independence result on cotorsion theories over valuation domains ⋮ Approximations and the little finitistic dimension of Artinian rings ⋮ Cotilting modules are pure-injective ⋮ Complete cotorsion pairs in exact categories ⋮ COMMUTING PROPERTIES OF EXT ⋮ Tilting theory and the finitistic dimension conjectures ⋮ Tilting modules over small Dedekind domains

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