… and isomorphism, and direct sum decompositions in C are “regular,” … endomorphism ring
of every module AR ∈ C is semilocal, that is, End(AR)/J (End(AR)) is a semisimple artinian ring, …

… In this survey, rings will be associative rings R with an identity, … We want to study direct-sum
decompositions of a module MR … modules relatively to directsum decompositions (Sects. 5.1…

… over Noetherian local rings and for direct-sum decompositions of Artinian modules… direct
sums of many copies of Pw and Qw, we will create these copies via a direct-sum decomposition …

… a direct sum of submodules with local endomorphism rings. … all of the Mi have local
endomorphism rings. In this setting, we … with applications to direct decomposition of modules, …

… ring E such that ErJ has exactly n simple modules, … Moreoer, E can be taken to be the
endomorphism ring of a finitely generated reflexie module oer a commutatie Noetherian local …

… He did this by showing that, over any ring, every artinian indecomposable module with
Loewy length ≤ ω has a local endomorphism ring. By the Krull-Schmidt-Remak-Azumaya …

… endomorphism rings. We analyze the peculiar behaviour of direct sum decomposition in
some categories of modules, where the uniqueness of the decomposition is obtained up …

… can have essentially different direct-sum decompositions as a direct sum of modules of …
direct sum M1 ⊕···⊕Mn of modules of type 2 can have direct summands that are not direct sums …

… endomorphisms and which works fundamentally with products of these decomposition
endomorphisms… may form the direct sum A of the abelian components and the direct sum J of the …

… endomorphism ring if and only if it is a finite direct sum of modules each of which has a local
endomorphism ring. … a regular endomorphism ring, but which admits a decomposition P=PX …