KERNELS OF MORPHISMS BETWEEN INDECOMPOSABLE INJECTIVE MODULES

DOI10.1017/S0017089510000170zbMath1210.16003OpenAlexW1979753192WikidataQ114117416 ScholiaQ114117416MaRDI QIDQ3577720

Alberto Facchini, Şule Ecevit, Muhammet Tamer Koşan

Publication date: 23 July 2010

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0017089510000170

zbMATH Keywords

endomorphism ringsKrull-Schmidt theoremindecomposable injective moduleskernels of endomorphisms

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Injective modules, self-injective associative rings (16D50) Automorphisms and endomorphisms (16W20)

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Auslander–Bridger 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 Krull-Schmidt theorem in the case two. ⋮ The Infinite Krull–Schmidt Property in the Case 2 ⋮ Direct-sum decompositions of modules with semilocal endomorphism rings ⋮ The Krull-Schmidt theorem holds for finite direct products of biuniform groups ⋮ On some noteworthy pairs of ideals in \(\mathrm{Mod-}R\) ⋮ On a category of extensions whose endomorphism rings have at most four maximal ideals ⋮ Cyclically Presented Modules Over Rings of Finite Type ⋮ Endomorphism Rings with Finitely Many Maximal Right Ideals ⋮ Direct products of modules whose endomorphism rings have at most two maximal ideals

Cites Work

• Injective modules over Noetherian rings
• Local morphisms and modules with a semilocal endomorphism ring.
• Equivalence of diagonal matrices over local rings.
• Serial modules and endomorphism rings
• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• Modules which are isomorphic to submodules of each other
• Krull-Schmidt fails for serial modules
• Almost Maximal Valuation Rings