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Keywords:
Cohen factorization; Gorenstein dimension; Gorenstein homomorphism; semi-dualizing complex
Cohen factorization; Gorenstein dimension; Gorenstein homomorphism; semi-dualizing complex
Summary:
We study the G-dimension over local ring homomorphisms with respect to a semi-dualizing complex. Some results that track the behavior of Gorenstein properties over local ring homomorphisms under composition and decomposition are given. As an application, we characterize a dualizing complex for $R$ in terms of the finiteness of the G-dimension over local ring homomorphisms with respect to a semi-dualizing complex.
References:
[1] Auslander, M., Bridger, M.: Stable Module Theory. Mem. Am. Math. Soc. 94 Providence (1969). MR 0269685 | Zbl 0204.36402
[2] Avramov, L. L., Foxby, H.-B.: Locally Gorenstein homomorphisms. Am. J. Math. 114 (1992), 1007-1047. DOI 10.2307/2374888 | MR 1183530 | Zbl 0769.13007
[3] Avramov, L. L., Foxby, H.-B.: Ring homomorphisms and finite Gorenstein dimension. Proc. Lond. Math. Soc. 75 (1997), 241-270. DOI 10.1112/S0024611597000348 | MR 1455856 | Zbl 0901.13011
[4] Avramov, L. L., Foxby, H.-B., Herzog, B.: Structure of local homomorphisms. J. Algebra 164 (1994), 124-145. DOI 10.1006/jabr.1994.1057 | MR 1268330 | Zbl 0798.13002
[5] Bennis, D., Mahdou, N.: First, second, and third change of rings theorems for Gorenstein homological dimensions. Commun. Algebra 38 (2010), 3837-3850. DOI 10.1080/00927870903286868 | MR 2760694 | Zbl 1205.13018
[6] Christensen, L. W.: Gorenstein Dimensions. Lecture Notes in Mathematics 1747 Sprin-ger, Berlin (2000). DOI 10.1007/BFb0103984 | MR 1799866 | Zbl 0965.13010
[7] Christensen, L. W.: Semi-dualizing complexes and their Auslander categories. Trans. Am. Math. Soc. 353 (2001), 1839-1883. DOI 10.1090/S0002-9947-01-02627-7 | MR 1813596 | Zbl 0969.13006
[8] Christensen, L. W., Holm, H.: Ascent properties of Auslander categories. Can. J. Math. 61 (2009), 76-108. DOI 10.4153/CJM-2009-004-x | MR 2488450 | Zbl 1173.13016
[9] Foxby, H.-B., Iyengar, S.: Depth and amplitude for unbounded complexes. Commutative Algebra. Interactions with Algebraic Geometry L. L. Avramov et al. Contemp. Math. 331 American Mathematical Society, Providence, RI (2003), 119-137. DOI 10.1090/conm/331/05906 | MR 2013162 | Zbl 1096.13516
[10] Iyengar, S.: Depth for complexes, and intersection theorems. Math. Z. 230 (1999), 545-567. DOI 10.1007/PL00004705 | MR 1680036 | Zbl 0927.13015
[11] Iyengar, S., Sather-Wagstaff, S.: G-dimension over local homomorphisms. Applications to the Frobenius endomorphism. Illinois J. Math. 48 (2004), 241-272. DOI 10.1215/ijm/1258136183 | MR 2048224 | Zbl 1103.13009
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