| Автор | Birkenmeier, Gary F. |
| Автор | Kim, Jin Yong |
| Автор | Park, Jae Keol |
| Дата выпуска | 1998 |
| dc.description | AbstractLet P be a prime ideal of a ring R, O(P) = {a ∊ R | aRs = 0, for some s ∊ R/P} | and Ō(P) = {x ∊ R | x<sup>n</sup> ∊ O(P), for some positive integer n}. Several authors have obtained sheaf representations of rings whose stalks are of the form R/O(P). Also in a commutative ring a minimal prime ideal has been characterized as a prime ideal P such that P= Ō(P). In this paper we derive various conditions which ensure that a prime ideal P = Ō(P). The property that P = Ō(P) is then used to obtain conditions which determine when R/O(P) has a unique minimal prime ideal. Various generalizations of O(P) and Ō(P) are considered. Examples are provided to illustrate and delimit our results. |
| Формат | application.pdf |
| Издатель | Cambridge University Press |
| Копирайт | Copyright © Glasgow Mathematical Journal Trust 1998 |
| Название | A characterization of minimal prime ideals |
| Тип | research-article |
| DOI | 10.1017/S0017089500032547 |
| Electronic ISSN | 1469-509X |
| Print ISSN | 0017-0895 |
| Журнал | Glasgow Mathematical Journal |
| Том | 40 |
| Первая страница | 223 |
| Последняя страница | 236 |
| Аффилиация | Birkenmeier Gary F.; University of Southwestern Louisiana |
| Аффилиация | Kim Jin Yong; Kyung Hee University |
| Аффилиация | Park Jae Keol; Busan National University |
| Выпуск | 2 |
