Simple modules over Auslander regular rings
In this paper, we discuss the properties of simple modules over Auslander regular rings with global dimension at most 3. Using grade theory, we show the right projective dimension of ExtΛ1(S,Λ)$\begin{array}{} \text{Ext}_{{\it\Lambda}}^{1}(S,\ {\it\Lambda}) \end{array} $ is equal to 1 for any simpl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-12-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0138/math-2017-0138.xml?format=INT |
| _version_ | 1818517232846635008 |
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| author | Huang Chonghui Zheng Lijing |
| author_facet | Huang Chonghui Zheng Lijing |
| author_sort | Huang Chonghui |
| collection | DOAJ |
| description | In this paper, we discuss the properties of simple modules over Auslander regular rings with global dimension at most 3. Using grade theory, we show the right projective dimension of
ExtΛ1(S,Λ)$\begin{array}{}
\text{Ext}_{{\it\Lambda}}^{1}(S,\ {\it\Lambda})
\end{array} $ is equal to 1 for any simple Λ-module S with gr S = 1. As a result, we give some equivalent characterization of diagonal Auslander regular rings. |
| first_indexed | 2024-12-11T00:53:29Z |
| format | Article |
| id | doaj.art-26ddde3688104d3e96ce97d90a88c3bc |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-11T00:53:29Z |
| publishDate | 2017-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-26ddde3688104d3e96ce97d90a88c3bc2022-12-22T01:26:33ZengDe GruyterOpen Mathematics2391-54552017-12-011511618162210.1515/math-2017-0138math-2017-0138Simple modules over Auslander regular ringsHuang Chonghui0Zheng Lijing1College of Mathematics and Physics, University of South China, Hengyang421001, ChinaCollege of Mathematics and Physics, University of South China, Hengyang421001, ChinaIn this paper, we discuss the properties of simple modules over Auslander regular rings with global dimension at most 3. Using grade theory, we show the right projective dimension of ExtΛ1(S,Λ)$\begin{array}{} \text{Ext}_{{\it\Lambda}}^{1}(S,\ {\it\Lambda}) \end{array} $ is equal to 1 for any simple Λ-module S with gr S = 1. As a result, we give some equivalent characterization of diagonal Auslander regular rings.http://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0138/math-2017-0138.xml?format=INTauslander regular ringdiagonal ringsimple modulegrade16e0516e10 |
| spellingShingle | Huang Chonghui Zheng Lijing Simple modules over Auslander regular rings Open Mathematics auslander regular ring diagonal ring simple module grade 16e05 16e10 |
| title | Simple modules over Auslander regular rings |
| title_full | Simple modules over Auslander regular rings |
| title_fullStr | Simple modules over Auslander regular rings |
| title_full_unstemmed | Simple modules over Auslander regular rings |
| title_short | Simple modules over Auslander regular rings |
| title_sort | simple modules over auslander regular rings |
| topic | auslander regular ring diagonal ring simple module grade 16e05 16e10 |
| url | http://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0138/math-2017-0138.xml?format=INT |
| work_keys_str_mv | AT huangchonghui simplemodulesoverauslanderregularrings AT zhenglijing simplemodulesoverauslanderregularrings |