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Unique decomposition of direct sums of ideals
| Title: | Unique decomposition of direct sums of ideals. |
 161 views 52 downloads |
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| Name(s): |
Ay, Basak. Charles E. Schmidt College of Science Department of Mathematical Sciences |
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| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Date Issued: | 2010 | |
| Publisher: | Florida Atlantic University | |
| Physical Form: | electronic | |
| Extent: | v, 47 p. : ill. | |
| Language(s): | English | |
| Summary: | 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. | |
| Identifier: | 650310509 (oclc), 2683133 (digitool), FADT2683133 (IID), fau:3491 (fedora) | |
| Note(s): |
by Basak Ay. Thesis (Ph.D.)--Florida Atlantic University, 2010. Includes bibliography. Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web. |
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| Subject(s): |
Algebraic number theory Modules (Algebra) Noetherian rings Commutative rings Algebra, Abstract |
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| Persistent Link to This Record: | http://purl.flvc.org/FAU/2683133 | |
| Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
| Host Institution: | FAU |
