Abstract
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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© 2009 Birkhäuser Verlag AG
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(2009). Indecomposable Modules. In: Regularity and Substructures of Hom. Frontiers in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9990-0_3
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DOI: https://doi.org/10.1007/978-3-7643-9990-0_3
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-9989-4
Online ISBN: 978-3-7643-9990-0
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