Some Properties of Noetherian Rings

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Description

This paper is an investigation of several basic properties of noetherian rings. Chapter I gives a brief introduction, statements of definitions, and statements of theorems without proof. Some of the main results in the study of noetherian rings are proved in Chapter II. These results include proofs of the equivalence of the maximal condition, the ascending chain condition, and that every ideal is finitely generated. Some other results are that if a ring R is noetherian, then R[x] is noetherian, and that if every prime ideal of a ring R is finitely generated, then R is noetherian.

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ii. 26 leaves

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Vaughan, Stephen N. (Stephen Nick) May 1986.

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This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 17 times . More information about this thesis can be viewed below.

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  • Vaughan, Stephen N. (Stephen Nick)

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Description

This paper is an investigation of several basic properties of noetherian rings. Chapter I gives a brief introduction, statements of definitions, and statements of theorems without proof. Some of the main results in the study of noetherian rings are proved in Chapter II. These results include proofs of the equivalence of the maximal condition, the ascending chain condition, and that every ideal is finitely generated. Some other results are that if a ring R is noetherian, then R[x] is noetherian, and that if every prime ideal of a ring R is finitely generated, then R is noetherian.

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ii. 26 leaves

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UNT Theses and Dissertations

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  • May 1986

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  • March 9, 2015, 8:15 a.m.

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  • Nov. 21, 2016, 1:27 p.m.

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Citations, Rights, Re-Use

Vaughan, Stephen N. (Stephen Nick). Some Properties of Noetherian Rings, thesis, May 1986; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc501109/: accessed October 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .