G-dimension over local homomorphisms with respect to a semi-dualizing complex

Wu Dejun

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 2, page 567-579
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Dejun, Wu. "G-dimension over local homomorphisms with respect to a semi-dualizing complex." Czechoslovak Mathematical Journal 64.2 (2014): 567-579. <http://eudml.org/doc/262033>.

@article{Dejun2014,
abstract = {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.},
author = {Dejun, Wu},
journal = {Czechoslovak Mathematical Journal},
keywords = {Cohen factorization; Gorenstein dimension; Gorenstein homomorphism; semi-dualizing complex; Cohen factorization; Gorenstein dimension; Gorenstein homomorphism; semi-dualizing complex},
language = {eng},
number = {2},
pages = {567-579},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {G-dimension over local homomorphisms with respect to a semi-dualizing complex},
url = {http://eudml.org/doc/262033},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Dejun, Wu
TI - G-dimension over local homomorphisms with respect to a semi-dualizing complex
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 567
EP - 579
AB - 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.
LA - eng
KW - Cohen factorization; Gorenstein dimension; Gorenstein homomorphism; semi-dualizing complex; Cohen factorization; Gorenstein dimension; Gorenstein homomorphism; semi-dualizing complex
UR - http://eudml.org/doc/262033
ER -

References

top
  1. Auslander, M., Bridger, M., Stable Module Theory, Mem. Am. Math. Soc. 94 Providence (1969). (1969) Zbl0204.36402MR0269685
  2. Avramov, L. L., Foxby, H.-B., 10.2307/2374888, Am. J. Math. 114 (1992), 1007-1047. (1992) Zbl0769.13007MR1183530DOI10.2307/2374888
  3. Avramov, L. L., Foxby, H.-B., 10.1112/S0024611597000348, Proc. Lond. Math. Soc. 75 (1997), 241-270. (1997) Zbl0901.13011MR1455856DOI10.1112/S0024611597000348
  4. Avramov, L. L., Foxby, H.-B., Herzog, B., 10.1006/jabr.1994.1057, J. Algebra 164 (1994), 124-145. (1994) Zbl0798.13002MR1268330DOI10.1006/jabr.1994.1057
  5. Bennis, D., Mahdou, N., 10.1080/00927870903286868, Commun. Algebra 38 (2010), 3837-3850. (2010) Zbl1205.13018MR2760694DOI10.1080/00927870903286868
  6. Christensen, L. W., 10.1007/BFb0103984, Lecture Notes in Mathematics 1747 Sprin-ger, Berlin (2000). (2000) Zbl0965.13010MR1799866DOI10.1007/BFb0103984
  7. Christensen, L. W., 10.1090/S0002-9947-01-02627-7, Trans. Am. Math. Soc. 353 (2001), 1839-1883. (2001) Zbl0969.13006MR1813596DOI10.1090/S0002-9947-01-02627-7
  8. Christensen, L. W., Holm, H., 10.4153/CJM-2009-004-x, Can. J. Math. 61 (2009), 76-108. (2009) Zbl1173.13016MR2488450DOI10.4153/CJM-2009-004-x
  9. Foxby, H.-B., Iyengar, S., 10.1090/conm/331/05906, Commutative Algebra. Interactions with Algebraic Geometry L. L. Avramov et al. Contemp. Math. 331 American Mathematical Society, Providence, RI (2003), 119-137. (2003) Zbl1096.13516MR2013162DOI10.1090/conm/331/05906
  10. Iyengar, S., 10.1007/PL00004705, Math. Z. 230 (1999), 545-567. (1999) Zbl0927.13015MR1680036DOI10.1007/PL00004705
  11. Iyengar, S., Sather-Wagstaff, S., 10.1215/ijm/1258136183, Illinois J. Math. 48 (2004), 241-272. (2004) Zbl1103.13009MR2048224DOI10.1215/ijm/1258136183

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.