Generalized tilting modules over ring extension

Zhen Zhang

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 3, page 801-810
  • ISSN: 0011-4642

Abstract

top
Let Γ be a ring extension of R . We show the left Γ -module U = Γ ⊗ R C with the endmorphism ring End Γ U = Δ is a generalized tilting module when R C is a generalized tilting module under some conditions.

How to cite

top

Zhang, Zhen. "Generalized tilting modules over ring extension." Czechoslovak Mathematical Journal 69.3 (2019): 801-810. <http://eudml.org/doc/294776>.

@article{Zhang2019,
abstract = {Let $ \Gamma $ be a ring extension of $R$. We show the left $\Gamma $-module $U=\Gamma \otimes _\{R\}C$ with the endmorphism ring End$_\{\Gamma \}U=\Delta $ is a generalized tilting module when $_\{R\}C$ is a generalized tilting module under some conditions.},
author = {Zhang, Zhen},
journal = {Czechoslovak Mathematical Journal},
keywords = {ring extension; generalized tilting module; faithfully balanced bimodule},
language = {eng},
number = {3},
pages = {801-810},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized tilting modules over ring extension},
url = {http://eudml.org/doc/294776},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Zhang, Zhen
TI - Generalized tilting modules over ring extension
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 3
SP - 801
EP - 810
AB - Let $ \Gamma $ be a ring extension of $R$. We show the left $\Gamma $-module $U=\Gamma \otimes _{R}C$ with the endmorphism ring End$_{\Gamma }U=\Delta $ is a generalized tilting module when $_{R}C$ is a generalized tilting module under some conditions.
LA - eng
KW - ring extension; generalized tilting module; faithfully balanced bimodule
UR - http://eudml.org/doc/294776
ER -

References

top
  1. Assem, I., Marmaridis, N., 10.1080/00927879808826219, Commun. Algebra 26 (1998), 1547-1555. (1998) Zbl0915.16007MR1622428DOI10.1080/00927879808826219
  2. 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
  3. Enochs, E. E., Jenda, O. M. G., 10.1515/9783110803662, De Gruyter Expositions in Mathematics 30, Walter de Gruyter, Berlin (2000). (2000) Zbl0952.13001MR1753146DOI10.1515/9783110803662
  4. Foxby, H.-B., 10.7146/math.scand.a-11434, Math. Scand. 31 (1972), 267-284. (1972) Zbl0272.13009MR0327752DOI10.7146/math.scand.a-11434
  5. Fuller, K. R., 10.1080/00927879708826026, Commun. Algebra 25 (1997), 2839-2860. (1997) Zbl0885.16019MR1458733DOI10.1080/00927879708826026
  6. Fuller, K. R., 10.1090/conm/259, Algebra and Its Applications Contemp. Math. 259, American Mathematical Society, Providence D. V. Huynh et al. (2000), 213-222. (2000) Zbl0965.16004MR1778503DOI10.1090/conm/259
  7. Göbel, R., Trlifaj, J., 10.1090/conm/259, De Gruyter Expositions in Mathematics 41, Walter De Gruyter, Berlin (2006). (2006) Zbl1121.16002MR2251271DOI10.1090/conm/259
  8. Golod, E. S., G -dimension and generalized perfect ideals, Tr. Mat. Inst. Steklova Russian 165 (1984), 62-66. (1984) Zbl0577.13008MR0752933
  9. Holm, H., White, D., 10.1215/kjm/1250692289, J. Math. Kyoto Univ. 47 (2007), 781-808. (2007) Zbl1154.16007MR2413065DOI10.1215/kjm/1250692289
  10. Miyashita, Y., 10.1007/BF01163359, Math. Z. 193 (1986), 113-146. (1986) Zbl0578.16015MR0852914DOI10.1007/BF01163359
  11. Sather-Wagstaff, S., Sharif, T., White, D., 10.1007/s00209-009-0480-4, Math. Z. 264 (2010), 571-600. (2010) Zbl1190.13007MR2591820DOI10.1007/s00209-009-0480-4
  12. Sather-Wagstaff, S., Sharif, T., White, D., 10.1016/j.jalgebra.2010.07.007, J. Algebra 324 (2010), 2336-2368. (2010) Zbl1207.13009MR2684143DOI10.1016/j.jalgebra.2010.07.007
  13. Sather-Wagstaff, S., Sharif, T., White, D., 10.1007/s10468-009-9195-9, Algebr. Represent. Theory 14 (2011), 403-428. (2011) Zbl1317.13029MR2785915DOI10.1007/s10468-009-9195-9
  14. Tonolo, A., 10.1515/form.2005.17.4.555, Forum Math. 17 (2005), 555-567. (2005) Zbl1088.16011MR2154419DOI10.1515/form.2005.17.4.555
  15. Vasconcelos, W. V., 10.1016/s0304-0208(08)x7021-5, North-Holland Mathematics Studies 14. Notas de Matematica 53, North-Holland Publishing, Amsterdam; American Elsevier Publishing Company, New York (1974). (1974) Zbl0296.13005MR0498530DOI10.1016/s0304-0208(08)x7021-5
  16. Wakamatsu, T., 10.1016/0021-8693(88)90215-3, J. Algebra 114 (1988), 106-114. (1988) Zbl0646.16025MR0931903DOI10.1016/0021-8693(88)90215-3
  17. Wakamatsu, T., 10.1016/0021-8693(90)90055-S, J. Algebra 134 (1990), 298-325. (1990) Zbl0726.16009MR1074331DOI10.1016/0021-8693(90)90055-S
  18. Wakamatsu, T., 10.1016/j.jalgebra.2003.12.008, J. Algebra 275 (2004), 3-39. (2004) Zbl1076.16006MR2047438DOI10.1016/j.jalgebra.2003.12.008
  19. Wei, J., 10.1016/j.jalgebra.2006.10.026, J. Algebra 310 (2007), 903-916. (2007) Zbl1118.16011MR2308185DOI10.1016/j.jalgebra.2006.10.026

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.