Representations of additive categories and direct-sum decompositions of objects

DOI10.1512/iumj.2007.56.2865zbMath1121.18007OpenAlexW2067487461MaRDI QIDQ5292682

Alberto Facchini

Publication date: 22 June 2007

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2007.56.2865

zbMATH Keywords

Krull-Schmidt propertyKrull monoidsplitting idempotentsdirect-summand reflecting functorIBN categoryKrull categoryreflecting functorskeletally small categoryunique direct-sum decomposition

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Preadditive, additive categories (18E05)

Related Items (12)

Auslander–Bridger Modules ⋮ Representations of quivers over a ring and the Weak Krull–Schmidt Theorems ⋮ Finite direct sums controlled by finitely many permutations. ⋮ Subdirect products of preadditive categories and weak equivalences ⋮ Morphisms determined by objects under Galois \(G\)-covering theory ⋮ MAXIMAL IDEALS IN PREADDITIVE CATEGORIES AND SEMILOCAL CATEGORIES ⋮ Direct-sum decompositions of modules with semilocal endomorphism rings ⋮ Direct summands of direct sums of modules whose endomorphism rings have two maximal right ideals. ⋮ On some noteworthy pairs of ideals in \(\mathrm{Mod-}R\) ⋮ Endomorphism Rings with Finitely Many Maximal Right Ideals ⋮ Direct products of modules whose endomorphism rings have at most two maximal ideals ⋮ Galois \(G\)-covering of quotients of linear categories

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