We say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains. In Chapters 1-3 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of one-dimensional reduced commutative Noetherian rings with the UDI property have the UDI property, also. In Chapter 5 we show that the UDI property implies the Krull-Schmidt property for direct sums of torsion-free rank one modules for a reduced local commutative Noetherian one-dimensional ring R. / by Basak Ay. / Thesis (Ph.D.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.
| Identifer | oai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_3491 |
| Contributors | Ay, Basak., Charles E. Schmidt College of Science, Department of Mathematical Sciences |
| Publisher | Florida Atlantic University |
| Source Sets | Florida Atlantic University |
| Language | English |
| Detected Language | English |
| Type | Text, Electronic Thesis or Dissertation |
| Format | v, 47 p. : ill., electronic |
| Rights | http://rightsstatements.org/vocab/InC/1.0/ |
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