| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 湯何曼 | zh_TW |
| DC.creator | Abdul Rahman Tambunan | en_US |
| dc.date.accessioned | 2017-1-16T07:39:07Z | |
| dc.date.available | 2017-1-16T07:39:07Z | |
| dc.date.issued | 2017 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=103221603 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.abstract | 這篇論文研究由P. M. Cohn 所提出之 generalized Euclidean ring（簡稱 GE-ring）的概念。當中也介紹了GE-ring 與 GE_n-ring（非GE-ring）的例子與其性質。從 Bass 的一項結果：「一個環 R 的 stable rank（表示成 sr(R)）與 GLn(R) 有關」可以得知，所有 stable rank 為 1 的環會是一個 GE-ring。另外有一事實則是一個主理想整環（principal ideal domain） 的 stable rank 則會小於等於 2。若一主理想整環的 stable rank 為 1，則其必為一歐幾里得環。文中也給出一些 stable rank 大於 1 之 GE-ring 的例子。對於在二次體（quadratic field） K=(Q√d)（其中d為一無平方數因數 square free）中的所有整數環（ring of integers, O_K），可以得到 sr(O_K)=2。 | zh_TW |
| dc.description.abstract | In this thesis, a generalized Euclidean ring, or GE-ring for short, a notion introduced by P. M. Cohn are studied. Properties and examples of GE-rings and GE_n-rings but not GE-rings are derived. Following the result of Bass, stable rank of a ring R (denoted by sr(R)) is related to the general linear group over R. Every ring with stable rank one is a GE-ring. A principal ideal domain (ring) has stable rank ? 2. For a principal ideal domain R with stable rank one, R must be a Euclidean ring. Examples of GE-rings with stable rank higher than one are given. For the ring of integers O_K in the quadratic field K = Q(√d) with d a square free rational integer, sr(O_K) = 2. | en_US |
| DC.subject | GE-ring | zh_TW |
| DC.subject | GE-ring | en_US |
| DC.subject | Generalized Euclidean Ring | en_US |
| DC.subject | Stable rank | en_US |
| DC.subject | Unimodular | en_US |
| DC.title | On Generalized Euclidean Rings | en_US |
| dc.language.iso | en_US | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |