Abstract
In the first two sections of this chapter we shall consider modules with the exchange property. Making use of the exchange property we shall study refinements of direct sum decompositions (Sections 2.3 and 2.10), prove the Krull- Schmidt-Remak-Azumaya Theorem (Section 2.4) and prove that every finitely presented module over a serial ring is serial (Section 3.5). If A,B,C are sub- modules of a module M and C ≤A, then A ∩ (B + C) = (A ∩ B) + C. This is called the modular identity. We begin with an immediate consequence of the modular identity that will be used repeatedly in the sequel.
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© 1998 Springer Basel AG
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Facchini, A. (1998). The Krull-Schmidt-Remak-Azumaya Theorem. In: Module Theory. Progress in Mathematics, vol 167. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8774-8_2
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DOI: https://doi.org/10.1007/978-3-0348-8774-8_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9769-3
Online ISBN: 978-3-0348-8774-8
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