The Krull-Schmidt theorem in the case two.

DOI10.1007/s10468-009-9202-1zbMath1259.16004OpenAlexW2033435765WikidataQ105357546 ScholiaQ105357546MaRDI QIDQ409232

Pavel Příhoda, Alberto Facchini

Publication date: 12 April 2012

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10468-009-9202-1

zbMATH Keywords

endomorphism ringsdirect-sum decompositionsfactor categoriescomplete bipartite graphssemilocal ringsweak Krull-Schmidt theorem

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) 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) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Noncommutative local and semilocal rings, perfect rings (16L30)

Related Items (10)

Homomorphisms with semilocal endomorphism rings between modules ⋮ Finite direct sums controlled by finitely many permutations. ⋮ On a category of chains of modules whose endomorphism rings have at most 2nmaximal ideals ⋮ Kernels of homomorphisms between uniform quasi-injective modules ⋮ The Infinite Krull–Schmidt Property in the Case 2 ⋮ 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 \(\mathrm{Mod-}R\) ⋮ On a category of extensions whose endomorphism rings have at most four maximal ideals ⋮ Direct products of modules whose endomorphism rings have at most two maximal ideals

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