Structure of semi-commutative π-regular rings(半交换π-正则环的结构)
引入了准体的概念，并用它刻画了半交换π-正则环的结构.证明了若R是半交换环，则下面条件是等价的：(1)R是π-正则环.(2)R的每个素理想均为极大理想.(3)R/PE(P)为准体，其中P为R的任意素理想，E(P)为P的所有幂等元素组成的集合.(4)P1，P2为R的两个素理想，若E(P1)=E(P2），则有P1=P2.并进一步证明了半交换π-正则环R同构于诸准体{R/PE(P)}的一个亚直接和，P∈M，M为R的所有素理想组成的集合....
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2008-07-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2008.04.002 |
| _version_ | 1797236260407869440 |
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| author | LUJian-wei(卢建伟) |
| author_facet | LUJian-wei(卢建伟) |
| author_sort | LUJian-wei(卢建伟) |
| collection | DOAJ |
| description | 引入了准体的概念，并用它刻画了半交换π-正则环的结构.证明了若R是半交换环，则下面条件是等价的：(1)R是π-正则环.(2)R的每个素理想均为极大理想.(3)R/PE(P)为准体，其中P为R的任意素理想，E(P)为P的所有幂等元素组成的集合.(4)P1，P2为R的两个素理想，若E(P1)=E(P2），则有P1=P2.并进一步证明了半交换π-正则环R同构于诸准体{R/PE(P)}的一个亚直接和，P∈M，M为R的所有素理想组成的集合. |
| first_indexed | 2024-04-24T17:01:02Z |
| format | Article |
| id | doaj.art-d55af59b51754741ac9307f8956f907e |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T17:01:02Z |
| publishDate | 2008-07-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-d55af59b51754741ac9307f8956f907e2024-03-29T01:58:25ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972008-07-0135436536810.3785/j.issn.1008-9497.2008.04.002Structure of semi-commutative π-regular rings(半交换π-正则环的结构)LUJian-wei(卢建伟)0College of Science, Shenyang University of Technology, Shenyang 110023, China(沈阳工业大学理学院，辽宁 沈阳 110023)引入了准体的概念，并用它刻画了半交换π-正则环的结构.证明了若R是半交换环，则下面条件是等价的：(1)R是π-正则环.(2)R的每个素理想均为极大理想.(3)R/PE(P)为准体，其中P为R的任意素理想，E(P)为P的所有幂等元素组成的集合.(4)P1，P2为R的两个素理想，若E(P1)=E(P2），则有P1=P2.并进一步证明了半交换π-正则环R同构于诸准体{R/PE(P)}的一个亚直接和，P∈M，M为R的所有素理想组成的集合.https://doi.org/10.3785/j.issn.1008-9497.2008.04.002半交换π-正则环幂等元素准素理想准体准无零因子环 |
| spellingShingle | LUJian-wei(卢建伟) Structure of semi-commutative π-regular rings(半交换π-正则环的结构) Zhejiang Daxue xuebao. Lixue ban 半交换π-正则环 幂等元素 准素理想 准体 准无零因子环 |
| title | Structure of semi-commutative π-regular rings(半交换π-正则环的结构) |
| title_full | Structure of semi-commutative π-regular rings(半交换π-正则环的结构) |
| title_fullStr | Structure of semi-commutative π-regular rings(半交换π-正则环的结构) |
| title_full_unstemmed | Structure of semi-commutative π-regular rings(半交换π-正则环的结构) |
| title_short | Structure of semi-commutative π-regular rings(半交换π-正则环的结构) |
| title_sort | structure of semi commutative π regular rings 半交换π 正则环的结构 |
| topic | 半交换π-正则环 幂等元素 准素理想 准体 准无零因子环 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2008.04.002 |
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