The Infinite Krull–Schmidt Property in the Case 2
DOI10.1080/00927872.2011.605819zbMath1287.16010OpenAlexW2016449755MaRDI QIDQ4909084
Publication date: 12 March 2013
Published in: Communications in Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00927872.2011.605819
categories of modulesdirect-sum decompositionsmonoidssemilocal ringsweak Krull-Schmidt theoremcocomplete categories
Module categories in associative algebras (16D90) 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) Preadditive, additive categories (18E05)
Cites Work
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- The Krull-Schmidt theorem in the case two.
- Equivalence of diagonal matrices over local rings.
- Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
- On uniserial modules that are not quasi-small.
- Weak Krull-Schmidt for infinite direct sums of cyclically presented modules over local rings.
- MAXIMAL IDEALS IN PREADDITIVE CATEGORIES AND SEMILOCAL CATEGORIES
- DIRECT SUMS OF INFINITELY MANY KERNELS
- KERNELS OF MORPHISMS BETWEEN INDECOMPOSABLE INJECTIVE MODULES
- Krull-Schmidt fails for serial modules
- PROJECTIVE MODULES AND DIVISOR HOMOMORPHISMS
- A Version of the Weak Krull–Schmidt Theorem for Infinite Direct Sums of Uniserial Modules
- Some model theory over a nearly simple uniserial domain and decompositions of serial modules
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