Krull-Remak-Schmidt decompositions in Hom-finite additive categories

DOI10.1016/j.exmath.2022.12.003OpenAlexW4313856887MaRDI QIDQ2695002

Amit Shah

Publication date: 30 March 2023

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.00337

zbMATH Keywords

idempotentadditive categoryKrull-Schmidt categoryHom-finite categoryKrull-Remak-Schmidt decompositionsplit idempotents

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) Noncommutative local and semilocal rings, perfect rings (16L30) Abelian categories, Grothendieck categories (18E10) Preadditive, additive categories (18E05) Idempotent elements (associative rings and algebras) (16U40)

Related Items (1)

Clifford's theorem for orbit categories

Cites Work

• Tame algebras and integral quadratic forms
• Krull-Schmidt categories and projective covers
• Unique decomposition and isomorphic refinement theorems in additive categories
• Almost split sequences and approximations
• Exact categories
• On the Krull-Schmidt theorem with application to sheaves
• Mathematicians under the Nazis
• Representation Theory of Artin Algebras I
• Algebras of Derived Dimension Zero
• Algèbres de Clifford et $K$-théorie
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