Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Gorenstein quasi-projective module; Gorenstein star module; Gorenstein tilting module
Gorenstein quasi-projective module; Gorenstein star module; Gorenstein tilting module
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.
References:
[1] Hügel, L. Angeleri, Coelho, F. U.: Infinitely generated tilting modules of finite projective dimension. Forum Math. 13 (2001), 239-250. DOI 10.1515/form.2001.006 | MR 1813669 | Zbl 0984.16009
[2] Auslander, M., Solberg, Ø.: Relative homology and representation theory I. Relative homology and homologically finite subcategories. Commun. Algebra 21 (1993), 2995-3031. DOI 10.1080/00927879308824717 | MR 1228751 | Zbl 0792.16017
[3] Bazzoni, S.: A characterization of $n$-cotilting and $n$-tilting modules. J. Algebra 273 (2004), 359-372. DOI 10.1016/S0021-8693(03)00432-0 | MR 2032465 | Zbl 1051.16007
[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. DOI 10.1007/BFb0088461 | MR 0607151 | Zbl 0446.16031
[5] Colpi, R., Trlifaj, J.: Tilting modules and tilting torsion theories. J. Algebra 178 (1995), 614-634. DOI 10.1006/jabr.1995.1368 | MR 1359905 | Zbl 0849.16033
[6] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra. de Gruyter Expositions in Mathematics 30. Walter de Gruyter, Berlin (2000). DOI 10.1515/9783110803662 | MR 1753146 | Zbl 0952.13001
[7] Happel, D., Ringel, C. M.: Tilted algebras. Trans. Am. Math. Soc. 274 (1982), 399-443. DOI 10.1090/S0002-9947-1982-0675063-2 | MR 0675063 | Zbl 0503.16024
[8] Holm, H.: Gorenstein homological dimensions. J. Pure Appl. Algebra 189 (2004), 167-193. DOI 10.1016/j.jpaa.2003.11.007 | MR 2038564 | Zbl 1050.16003
[9] Wei, J.: $n$-star modules and $n$-tilting modules. J. Algebra 283 (2005), 711-722. DOI 10.1016/j.jalgebra.2004.09.032 | MR 2111219 | Zbl 1112.16011
[10] Wei, J.: A note on relative tilting modules. J. Pure Appl. Algebra 214 (2010), 493-500. DOI 10.1016/j.jpaa.2009.06.018 | MR 2558755 | Zbl 1185.16011
[11] Yan, L., Li, W., Ouyang, B.: Gorenstein cotilting and tilting modules. Commun. Algebra 44 (2016), 591-603. DOI 10.1080/00927872.2014.981752 | MR 3449939 | Zbl 1344.16008
Search
Partner of
