Idempotent functors and localizations in categories of modules and Abelian groups.
DOI10.1007/s10958-012-0818-zzbMath1264.16005OpenAlexW2040746190MaRDI QIDQ690756
Piotr A. Krylov, Askar A. Tuganbaev
Publication date: 29 November 2012
Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10958-012-0818-z
categories of Abelian groupsnatural transformationsE-ringsendofunctorsE-modulesidempotent functorslocalizations in module categorieslocalizations of Abelian groupsT-rings
Module categories in associative algebras (16D90) Torsion theories, radicals (18E40) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Homological and categorical methods for abelian groups (20K40) Localization of categories, calculus of fractions (18E35) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)
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Cites Work
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- Localizations and adjointness
- Classifying \(E\)-algebras over Dedekind domains.
- Projective and generating modules over the ring of pseudorational numbers.
- On radicals and products
- Torsion-free E-modules
- Colocalization and localization in Abelian categories
- Equivalence between colocalization and localization in Abelian categories with applications to the theory of modules
- Large \(E\)-modules exist
- The localization of spaces with respect to homology
- Constructions of factorization systems in categories
- Colocalization and localization
- Duality between colocalization and localization
- Two-sided E-rings.
- \(M\)-free Abelian groups.
- Cardinality and nilpotency of localizations of groups and \(G\)-modules
- Localizations of torsion-free Abelian groups. II.
- Relative group completions
- Large E-rings exist
- Properties of endomorphism rings of Abelian groups. II.
- Localizations of torsion-free Abelian groups.
- Cellular spaces, null spaces and homotopy localization
- The center of the endomorphism ring of a split mixed Abelian group
- Quasi-localizations of \(\mathbb{Z}\).
- Approximations and endomorphism algebras of modules.
- Modules over discrete valuation domains. II
- Homomorphisms and duality for torsion-free groups
- Homotopy limits, completions and localizations
- Almost-free E(R)-algebras and E(A,R)-modules
- Homotopy localization of groupoids
- Homotopical localizations of spaces
- A-Rings
- $E$-algebras whose torsion part is not cyclic
- Self-Free Modules and E-Rings
- On localizations of torsion abelian groups
- The Existence of LargeE(R)-Algebras That Are Sharply Transitive Modules
- The endomorphism ring of the additive group of a ring
- SuperdecomposableE(R)-Algebras
- Rings and modules of quotients
- Abelian groups and regular modules
