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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc501109 |
| Date | 05 1900 |
| Creators | Vaughan, Stephen N. (Stephen Nick) |
| Contributors | Vaughan, Nick H., Lewis, Paul Weldon |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | ii. 26 leaves, Text |
| Rights | Public, Vaughan, Stephen N. (Stephen Nick), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
Page generated in 0.0022 seconds