Publisher Summary This chapter provides an overview of the basic concepts of the Krull-
Schmidt theorem. The two proofs of the Krull-Schmidt-Azumaya theorem, mention …

A Krull–Schmidt theorem for infinite products of modules - ScienceDirect Skip to main
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M s [M s [N are two indecomposable decompositions of aij ig I jg J module M, where M has
local endomorphism ring for each ig I, then i there is a bijection: I ª J such that M (N for every …

It is well known that if a module M is expressible as a direct sum of modules with local
endomorphism rings, then such a decomposition is essentially unique. That is, if M=⊕ i∊ …

Commutative monoids yield an analogy between the theory of factorization in commutative
integral domains and the theory of direct sum decompositions of modules. We show that the …

Let (R, m) be a local ring (commutative and Noetherian). If R is complete (or, more generally,
Henselian), one has the Krull–Schmidt uniqueness theorem for direct sums of …

We study what happens if, in the Krull-Schmidt Theorem, instead of considering modules
whose endomorphism rings have one maximal ideal, we consider modules whose …

In 1-4] Nakayama proved that every module M over a generalized uniserial ring has a
decomposition M=~) M~ in which each term is A uniserial (ie, its submodules form a chain) …

Full article: A Version of the Weak Krull–Schmidt Theorem for Infinite Direct Sums of Uniserial
Modules Skip to Main Content Taylor and Francis Online homepage Taylor and Francis …

The well-known Krull–Schmidt–Azumaya theorem gives sufficient conditions for a module to
have an essentially unique decomposition as a direct sum of indecomposable submodules …