Two results on modules whose endomorphism ring is semilocal.

DOI10.1023/B:ALGE.0000048320.11088.49zbMath1077.16007OpenAlexW2051569392MaRDI QIDQ1770890

Alberto Facchini, Herbera, Dolors

Publication date: 7 April 2005

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

Full work available at URL: https://doi.org/10.1023/b:alge.0000048320.11088.49

zbMATH Keywords

endomorphism ringsfinitely generated modulesdirect sumsdirect summandsKrull-Schmidt theoremsemilocal ringsdual Goldie dimension

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) 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)

Related Items (9)

Unnamed Item ⋮ On a generalization of the exchange property to modules with semilocal endomorphism rings. ⋮ On a category of chains of modules whose endomorphism rings have at most 2nmaximal ideals ⋮ The Krull-Schmidt theorem in the case two. ⋮ MAXIMAL IDEALS IN PREADDITIVE CATEGORIES AND SEMILOCAL CATEGORIES ⋮ Direct-sum decompositions of modules with semilocal endomorphism rings ⋮ On some noteworthy pairs of ideals in \(\mathrm{Mod-}R\) ⋮ A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems ⋮ Direct sum decompositions of modules, semilocal endomorphism rings, and Krull monoids

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