Date of Award
2010
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
Abstract
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.
Extent
v, 47 p. : ill.
Recommended Citation
Ay, Basak., "Unique decomposition of direct sums of ideals" (2010). Electronic Theses and Dissertations 2010 - 2019. 204.
https://digitalcommons.fau.edu/etd_general_6/204
Identifier
FADT2683133
Comments
by Basak Ay.|Thesis (Ph.D.)--Florida Atlantic University, 2010.|Includes bibliography.|Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.|by Basak Ay.