| Title:
|
Gorenstein star modules and Gorenstein tilting modules (English) |
| Author:
|
Zhang, Peiyu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
403-416 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the notion of Gorenstein star modules and obtain some properties and a characterization of them. We mainly give the relationship between $n$-Gorenstein star modules and $n$-Gorenstein tilting modules, see L. Yan, W. Li, B. Ouyang (2016), and a new characterization of $n$-Gorenstein tilting modules. (English) |
| Keyword:
|
Gorenstein quasi-projective module |
| Keyword:
|
Gorenstein star module |
| Keyword:
|
Gorenstein tilting module |
| MSC:
|
16D90 |
| MSC:
|
18E40 |
| MSC:
|
18G05 |
| MSC:
|
18G15 |
| idZBL:
|
07361076 |
| idMR:
|
MR4263177 |
| DOI:
|
10.21136/CMJ.2020.0395-19 |
| . |
| Date available:
|
2021-05-20T13:42:01Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148912 |
| . |
| Reference:
|
[1] Hügel, L. Angeleri, Coelho, F. U.: Infinitely generated tilting modules of finite projective dimension.Forum Math. 13 (2001), 239-250. Zbl 0984.16009, MR 1813669, 10.1515/form.2001.006 |
| Reference:
|
[2] Auslander, M., Solberg, Ø.: Relative homology and representation theory I. Relative homology and homologically finite subcategories.Commun. Algebra 21 (1993), 2995-3031. Zbl 0792.16017, MR 1228751, 10.1080/00927879308824717 |
| Reference:
|
[3] Bazzoni, S.: A characterization of $n$-cotilting and $n$-tilting modules.J. Algebra 273 (2004), 359-372. Zbl 1051.16007, MR 2032465, 10.1016/S0021-8693(03)00432-0 |
| Reference:
|
[4] Brenner, S., Butler, M. C. R.: Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors.Representation Theory II Lecture Notes in Mathematics 832. Springer, Berlin (1980), 103-169. Zbl 0446.16031, MR 0607151, 10.1007/BFb0088461 |
| Reference:
|
[5] Colpi, R., Trlifaj, J.: Tilting modules and tilting torsion theories.J. Algebra 178 (1995), 614-634. Zbl 0849.16033, MR 1359905, 10.1006/jabr.1995.1368 |
| Reference:
|
[6] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra.de Gruyter Expositions in Mathematics 30. Walter de Gruyter, Berlin (2000). Zbl 0952.13001, MR 1753146, 10.1515/9783110803662 |
| Reference:
|
[7] Happel, D., Ringel, C. M.: Tilted algebras.Trans. Am. Math. Soc. 274 (1982), 399-443. Zbl 0503.16024, MR 0675063, 10.1090/S0002-9947-1982-0675063-2 |
| Reference:
|
[8] Holm, H.: Gorenstein homological dimensions.J. Pure Appl. Algebra 189 (2004), 167-193. Zbl 1050.16003, MR 2038564, 10.1016/j.jpaa.2003.11.007 |
| Reference:
|
[9] Wei, J.: $n$-star modules and $n$-tilting modules.J. Algebra 283 (2005), 711-722. Zbl 1112.16011, MR 2111219, 10.1016/j.jalgebra.2004.09.032 |
| Reference:
|
[10] Wei, J.: A note on relative tilting modules.J. Pure Appl. Algebra 214 (2010), 493-500. Zbl 1185.16011, MR 2558755, 10.1016/j.jpaa.2009.06.018 |
| Reference:
|
[11] Yan, L., Li, W., Ouyang, B.: Gorenstein cotilting and tilting modules.Commun. Algebra 44 (2016), 591-603. Zbl 1344.16008, MR 3449939, 10.1080/00927872.2014.981752 |
| . |
