Semiclean rings and their extensions(Semiclean环及其扩张)
对clean环进行了推广，研究了 semiclean环，讨论了 semiclean环的几个重要性质；证明了(1)R是semi-clean 环;(2)R上的形式幂级数环R[[x]]是semiclean环；(3)R上的斜幂级数环R[[x;α]是semiclean环等价；最后证明了，如果R是环，(S，≤)是严格偏序幺半群且对任意s∈S，都有0≤s，则[[RS, ≤]]是semiclean环当且仅当R是semiclean环....
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | zho |
| Published: |
Zhejiang University Press
2012-01-01
|
| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2012.01.002 |
| _version_ | 1797236060702375936 |
|---|---|
| author | GUOLi-qin(郭莉琴) WANGGuo-jun(汪国军) |
| author_facet | GUOLi-qin(郭莉琴) WANGGuo-jun(汪国军) |
| author_sort | GUOLi-qin(郭莉琴) |
| collection | DOAJ |
| description | 对clean环进行了推广，研究了 semiclean环，讨论了 semiclean环的几个重要性质；证明了(1)R是semi-clean 环;(2)R上的形式幂级数环R[[x]]是semiclean环；(3)R上的斜幂级数环R[[x;α]是semiclean环等价；最后证明了，如果R是环，(S，≤)是严格偏序幺半群且对任意s∈S，都有0≤s，则[[RS, ≤]]是semiclean环当且仅当R是semiclean环. |
| first_indexed | 2024-04-24T16:57:51Z |
| format | Article |
| id | doaj.art-ad85d6550675488dbd40f7686275af8c |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:57:51Z |
| publishDate | 2012-01-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-ad85d6550675488dbd40f7686275af8c2024-03-29T01:58:30ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972012-01-013914810.3785/j.issn.1008-9497.2012.01.002Semiclean rings and their extensions(Semiclean环及其扩张)GUOLi-qin(郭莉琴)0WANGGuo-jun(汪国军)1 1.School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, Gansu Province, China( 1.天水师范学院数学与统计学院，甘肃 天水 741001) 2.Department of Mathematics, Zhejiang University, Hangzhou 310027, China( 2.浙江大学数学系，浙江 杭州 310027)对clean环进行了推广，研究了 semiclean环，讨论了 semiclean环的几个重要性质；证明了(1)R是semi-clean 环;(2)R上的形式幂级数环R[[x]]是semiclean环；(3)R上的斜幂级数环R[[x;α]是semiclean环等价；最后证明了，如果R是环，(S，≤)是严格偏序幺半群且对任意s∈S，都有0≤s，则[[RS, ≤]]是semiclean环当且仅当R是semiclean环.https://doi.org/10.3785/j.issn.1008-9497.2012.01.002clean环semiclean环形式幂级数环斜幂级数环广义幂级数环 |
| spellingShingle | GUOLi-qin(郭莉琴) WANGGuo-jun(汪国军) Semiclean rings and their extensions(Semiclean环及其扩张) Zhejiang Daxue xuebao. Lixue ban clean环 semiclean环 形式幂级数环 斜幂级数环 广义幂级数环 |
| title | Semiclean rings and their extensions(Semiclean环及其扩张) |
| title_full | Semiclean rings and their extensions(Semiclean环及其扩张) |
| title_fullStr | Semiclean rings and their extensions(Semiclean环及其扩张) |
| title_full_unstemmed | Semiclean rings and their extensions(Semiclean环及其扩张) |
| title_short | Semiclean rings and their extensions(Semiclean环及其扩张) |
| title_sort | semiclean rings and their extensions semiclean环及其扩张 |
| topic | clean环 semiclean环 形式幂级数环 斜幂级数环 广义幂级数环 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2012.01.002 |
| work_keys_str_mv | AT guoliqinguōlìqín semicleanringsandtheirextensionssemicleanhuánjíqíkuòzhāng AT wangguojunwāngguójūn semicleanringsandtheirextensionssemicleanhuánjíqíkuòzhāng |