Uniqueness of monogeny classes for uniform objects in abelian categories
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Publication:1612144
DOI10.1016/S0022-4049(01)00160-8zbMath1006.18010MaRDI QIDQ1612144
Luca Diracca, Alberto Facchini
Publication date: 22 August 2002
Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)
Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Abelian categories, Grothendieck categories (18E10) Directed graphs (digraphs), tournaments (05C20)
Related Items (13)
Local morphisms and modules with a semilocal endomorphism ring. ⋮ On a category of chains of modules whose endomorphism rings have at most 2nmaximal ideals ⋮ Uniqueness of uniform decompositions in abelian categories ⋮ Monogeny dimension relative to a fixed uniform module. ⋮ Equivalence of diagonal matrices over local rings. ⋮ Direct-sum decompositions of modules with semilocal endomorphism rings ⋮ Uniqueness of uniform decompositions in exact categories ⋮ Direct summands of direct sums of modules whose endomorphism rings have two maximal right ideals. ⋮ On a category of extensions whose endomorphism rings have at most four maximal ideals ⋮ A uniqueness theorem in a finitely accessible additive category ⋮ Cyclically Presented Modules Over Rings of Finite Type ⋮ On pure Goldie dimensions ⋮ Direct sum decompositions of modules, semilocal endomorphism rings, and Krull monoids
Cites Work
- Quasi-isomorphisms of finitely generated modules over valuation domains
- Weak Krull-Schmidt for infinite direct sums of uniserial modules
- Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
- On Direct Decomposition of Torsion Free Abelian Groups.
- Krull-Schmidt fails for serial modules
- Krull-Schmidt Fails for Artinian Modules
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