Abstract:
Let G,H be groups, φ:G→H a group morphism, and A a G-graded algebra. The morphism φ induces an H-grading on A, and on any G-graded A-module, which thus becomes an H-graded A-module. Given an injective G-graded A-module, we give bounds for its injective dimension when seen as H-graded A-module. Following ideas by Van den Bergh, we give an application of our results to the stability of dualizing complexes through change of grading. © 2018, © 2018 Taylor & Francis.
Registro:
Documento: |
Artículo
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Título: | Change of grading, injective dimension and dualizing complexes |
Autor: | Solotar, A.; Zadunaisky, P. |
Filiación: | IMAS-CONICET y Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, Argentina Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil
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Palabras clave: | Change of grading; dualizing complexes; injective modules |
Año: | 2018
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Volumen: | 46
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Número: | 10
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Página de inicio: | 4414
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Página de fin: | 4425
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DOI: |
http://dx.doi.org/10.1080/00927872.2018.1444170 |
Título revista: | Communications in Algebra
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Título revista abreviado: | Commun. Algebra
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ISSN: | 00927872
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00927872_v46_n10_p4414_Solotar |
Referencias:
- Chin, W., Quinn, D., Rings graded by polycyclic-by-finite groups (1988) Proc. Am. Math. Soc., 102 (2), pp. 235-241
- Ekström, E.K., (1989) The Auslander Condition on Graded and Filtered Noetherian Rings, 1404, pp. 220-245. , Année (Paris, 1987/1988). Lecture Notes Mathematics, Berlin: Springer
- Faith, C., Walker, E.A., Direct-sum representations of injective modules (1967) J. Algebra, 5, pp. 203-221
- Fossum, R., Foxby, H.-B., The category of graded modules (1974) Math. Scand., 35, pp. 288-300
- Goodearl, K.R., Warfield Jr, R.B., (2004) An Introduction to Noncommutative Noetherian Rings, 61. , 2nd ed., London Mathematical Society Student Texts, Cambridge: Cambridge University Press
- Hartshorne, R., (1966) Residues and Duality, 20. , Lecture Notes of a Seminar on the Work of A. Grothendieck, Given at Harvard 1963/64. With an Appendix by P. Deligne. Lecture Notes Mathematics, Berlin: Springer-Verlag
- Jørgensen, P., Local cohomology for non-commutative graded algebras (1997) Comm. Algebra, 25 (2), pp. 575-591
- Levasseur, T., Some properties of noncommutative regular graded rings (1992) Glasgow Math. J., 34 (3), pp. 277-300
- Montgomery, S., Hopf algebras and their actions on rings (1993) CBMS Regional Conference Series in Mathematics, 82. , Published for the Conference Board of the Mathematical Sciences, Washington, DC:. In
- Năstăsescu, C., Van Oystaeyen, F., (2004) Methods of Graded Rings, , Lecture Notes Mathematics, 1836, Berlin: Springer-Verlag
- Polishchuk, A., Positselski, L., Hochschild (co)homology of the second kind I (2012) Trans. Am. Math. Soc., 364 (10), pp. 5311-5368
- Rigal, L., Zadunaisky, P., Twisted semigroup algebras (2015) Alg. Rep. Theory, 5, pp. 1155-1186
- van den Bergh, M., Existence theorems for dualizing complexes over non-commutative graded and filtered rings (1997) J. Algebra, 195 (2), pp. 662-679
- Wu, Q.-S., Zhang, J.J., Applications of dualizing complexes (2002) Proceedings of the Third International Algebra Conference, pp. 241-255. , Tainan, Kluwer Acad. Publ., Dordrecht:. In
- Yekutieli, A., Dualizing complexes over noncommutative graded algebras (1992) J. Algebra, 153 (1), pp. 41-84
- Yekutieli, A., (2014), http://arxiv.org/abs/1407.5916, Another proof of a theorem of Van den Bergh about graded-injective modules; Yekutieli, A., Zhang, J.J., Rings with Auslander dualizing complexes (1999) J. Algebra, 213 (1), pp. 1-51
- Yekutieli, A., Zhang, J.J., Rigid dualizing complexes over commutative rings (2009) Algebr. Represent. Theory, 12 (1), pp. 19-52
- Zadunaisky, P., (2014), http://cms.dm.uba.ar/academico/carreras/doctorado/desde, Homological regularity properties of quantum flag varieties and related algebras. Ph.D. Thesis
Citas:
---------- APA ----------
Solotar, A. & Zadunaisky, P.
(2018)
. Change of grading, injective dimension and dualizing complexes. Communications in Algebra, 46(10), 4414-4425.
http://dx.doi.org/10.1080/00927872.2018.1444170---------- CHICAGO ----------
Solotar, A., Zadunaisky, P.
"Change of grading, injective dimension and dualizing complexes"
. Communications in Algebra 46, no. 10
(2018) : 4414-4425.
http://dx.doi.org/10.1080/00927872.2018.1444170---------- MLA ----------
Solotar, A., Zadunaisky, P.
"Change of grading, injective dimension and dualizing complexes"
. Communications in Algebra, vol. 46, no. 10, 2018, pp. 4414-4425.
http://dx.doi.org/10.1080/00927872.2018.1444170---------- VANCOUVER ----------
Solotar, A., Zadunaisky, P. Change of grading, injective dimension and dualizing complexes. Commun. Algebra. 2018;46(10):4414-4425.
http://dx.doi.org/10.1080/00927872.2018.1444170