Current Search: Omairi, Akeel (x)
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Title
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H-LOCAL RINGS.
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Creator
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Omairi, Akeel, Klingler, Lee, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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We say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a _nite 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 and in a 2011 paper Ay and Klingler obtain similar results for Noetherian reduced rings. We characterize the UDI property for Noetherian...
Show moreWe say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a _nite 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 and in a 2011 paper Ay and Klingler obtain similar results for Noetherian reduced rings. We characterize the UDI property for Noetherian rings in general.
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Date Issued
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2019
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PURL
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http://purl.flvc.org/fau/fd/FA00013336
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Subject Headings
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Noetherian rings, Prüfer rings, Local rings
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Format
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Document (PDF)
