Abstract
It is shown that there is a connection between Roth's theorems on similarity and equivalence of block-triangular matrices and decomposition of modules. The module property is that if M≅ N⊕M N , then N is a summand of M . This holds for any commutative ring if M is finitely presented. New proofs of Roth's theorems are given for commutative rings. Some results are established in the noncommutative case.
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