|
|||||
|
|
| 两类整环在w-算子下的刻画 | |
| 引用本文： | 陈幼华,尹华玉.两类整环在w-算子下的刻画[J].数学学报,2010,53(4):685-690. |
| 作者姓名： | 陈幼华 尹华玉 |
| 作者单位： | 1. 四川师范大学数学与软件科学学院 成都 610068; 2. 南京大学数学系 南京 210093 |
| 基金项目： | 国家自然科学基金资助项目(10671137,10971090);四川省重点学科建设基金资助项目(SZD0406);四川师范大学科研基金资助项目(08QNL09) |
| 摘 要： | 通过对SM整环中准素w-理想与w-互素理想的讨论,证明了R是Krull整环当且仅当R是SM整环,w-dim(R)=1,且每个p-准素w-理想是素理想p的幂的w-包络.同时,运用w-算子,辅以t-,v-算子给出了π-整环的一些新的等价刻画. |
| 关 键 词： | w-互素 SM整环 Krull整环 π-整环 |
| 收稿时间： | 2008-12-09 |
| 修稿时间： | 2010-01-20 |
Characterizations of Two Classes of Domains Under the w-Operations |
|
| Institution: | 1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, P. R. China; 2. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China |
| Abstract: | In this paper, we discuss the primary w-ideals and the w-coprime ideals in SM domains, and prove that R is a Krull domain if and only if R is an SM domain with w-dim(R)=1, and every  -primary w-ideal of R is a w-envelope of some power of the prime ideal . Moreover, we show some new equivalent characterizations of π-domains by utilizing w-operations and with the supplement of t- and v-operations.
|
| Keywords: | w-coprime SM domain Krull domain &pi -domain |
| 点击此处可从《数学学报》浏览原始摘要信息 | |
| 点击此处可从《数学学报》下载免费的PDF全文 | |