Silting Complexes and Partial Tilting Modules
It is well known that a partial tilting module may not be completed to a tilting module. However, it is still unknown whether a partial tilting module can be completed to a silting complex. The affirmative answer to this question will give an affirmative answer to the well-known rank question for ti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1736 |
| _version_ | 1827704646764855296 |
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| author | Jiaqun Wei |
| author_facet | Jiaqun Wei |
| author_sort | Jiaqun Wei |
| collection | DOAJ |
| description | It is well known that a partial tilting module may not be completed to a tilting module. However, it is still unknown whether a partial tilting module can be completed to a silting complex. The affirmative answer to this question will give an affirmative answer to the well-known rank question for tilting modules. In this paper, we prove that a partial tilting simple module can always be completed to a silting complex. More generally, we give the sufficient conditions for a partial tilting module to be completed to a silting complex. |
| first_indexed | 2024-03-10T15:44:48Z |
| format | Article |
| id | doaj.art-d3878f6e10dc41a5bb600618b0ee55e6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:44:48Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d3878f6e10dc41a5bb600618b0ee55e62023-11-20T16:35:40ZengMDPI AGMathematics2227-73902020-10-01810173610.3390/math8101736Silting Complexes and Partial Tilting ModulesJiaqun Wei0Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaIt is well known that a partial tilting module may not be completed to a tilting module. However, it is still unknown whether a partial tilting module can be completed to a silting complex. The affirmative answer to this question will give an affirmative answer to the well-known rank question for tilting modules. In this paper, we prove that a partial tilting simple module can always be completed to a silting complex. More generally, we give the sufficient conditions for a partial tilting module to be completed to a silting complex.https://www.mdpi.com/2227-7390/8/10/1736partial tilting modulesilting complexcomplementsimple module |
| spellingShingle | Jiaqun Wei Silting Complexes and Partial Tilting Modules Mathematics partial tilting module silting complex complement simple module |
| title | Silting Complexes and Partial Tilting Modules |
| title_full | Silting Complexes and Partial Tilting Modules |
| title_fullStr | Silting Complexes and Partial Tilting Modules |
| title_full_unstemmed | Silting Complexes and Partial Tilting Modules |
| title_short | Silting Complexes and Partial Tilting Modules |
| title_sort | silting complexes and partial tilting modules |
| topic | partial tilting module silting complex complement simple module |
| url | https://www.mdpi.com/2227-7390/8/10/1736 |
| work_keys_str_mv | AT jiaqunwei siltingcomplexesandpartialtiltingmodules |