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 Unique decomposition of direct sums of ideals.


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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.

Subject(s): Algebraic number theoryModules (Algebra)Noetherian ringsCommutative ringsAlgebra, Abstract

Persistent Link to This Record: http://purl.flvc.org/FAU/2683133

Owner Institution: FAU



Autor: Ay, Basak.

Fuente: http://fau.digital.flvc.org/islandora/object/fau%3A3491



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