Indecomposable Modules

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Duration: 3 min 30 s
Description: A module M is directly indecomposable (or simply indecomposable) if and only if 0 and M are the only direct summands of M. This means that 0 and 1 are the only idempotents in End(MR). We now study the situation that Reg(A, M) ≠ 0 and one of the modules A or M is indecomposable. It turns out that much can be said under assumptions weaker than Reg(A, M) ≠ 0.
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