Direct sum decompositions of modules, semilocal endomorphism rings, and Krull monoids
A Facchini - Journal of Algebra, 2002 - Elsevier
… 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, …
of every module AR ∈ C is semilocal, that is, End(AR)/J (End(AR)) is a semisimple artinian ring, …
Direct-sum decompositions of modules with semilocal endomorphism rings
A Facchini - Bulletin of Mathematical Sciences, 2012 - Springer
… 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…
decompositions of a module MR … modules relatively to directsum decompositions (Sects. 5.1…
[PDF][PDF] Direct-sum decompositions of modules with semilocal endomorphism rings
A Facchini, R Wiegand - Journal of Algebra, 2004 - researchgate.net
… 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 …
sums of many copies of Pw and Qw, we will create these copies via a direct-sum decomposition …
Direct sums of representations as modules over their endomorphism rings
B Huisgen-Zimmermann, M Saorín - arXiv preprint arXiv:1407.2364, 2014 - arxiv.org
… 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, …
endomorphism rings. In this setting, we … with applications to direct decomposition of modules, …
Direct-sum decompositions over local rings
R Wiegand - Journal of Algebra, 2001 - Elsevier
… 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 …
endomorphism ring of a finitely generated reflexie module oer a commutatie Noetherian local …
[图书][B] Module theory: endomorphism rings and direct sum decompositions in some classes of modules
A Facchini - 2012 - books.google.com
… 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 …
Loewy length ≤ ω has a local endomorphism ring. By the Krull-Schmidt-Remak-Azumaya …
Direct sum decompositions and weak Krull-Schmidt Theorems
M Perone - 2011 - research.unipd.it
… 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 …
some categories of modules, where the uniqueness of the decomposition is obtained up …
Direct summands of direct sums of modules whose endomorphism rings have two maximal right ideals
A Amini, B Amini, A Facchini - Journal of Pure and Applied Algebra, 2011 - Elsevier
… 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 …
direct sum M1 ⊕···⊕Mn of modules of type 2 can have direct summands that are not direct sums …
Direct decompositions
R Baer - Transactions of the American Mathematical Society, 1947 - JSTOR
… 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 …
endomorphisms… may form the direct sum A of the abelian components and the direct sum J of the …
Endomorphism rings of projective modules
R Ware - Transactions of the American Mathematical Society, 1971 - ams.org
… 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 …
endomorphism ring. … a regular endomorphism ring, but which admits a decomposition P=PX …
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