C -Gorenstein projective, injective and flat modules

Xiao Yan Yang; Zhong Kui Liu

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 4, page 1109-1129
  • ISSN: 0011-4642

Abstract

top
By analogy with the projective, injective and flat modules, in this paper we study some properties of C -Gorenstein projective, injective and flat modules and discuss some connections between C -Gorenstein injective and C -Gorenstein flat modules. We also investigate some connections between C -Gorenstein projective, injective and flat modules of change of rings.

How to cite

top

Yang, Xiao Yan, and Liu, Zhong Kui. "$C$-Gorenstein projective, injective and flat modules." Czechoslovak Mathematical Journal 60.4 (2010): 1109-1129. <http://eudml.org/doc/196860>.

@article{Yang2010,
abstract = {By analogy with the projective, injective and flat modules, in this paper we study some properties of $C$-Gorenstein projective, injective and flat modules and discuss some connections between $C$-Gorenstein injective and $C$-Gorenstein flat modules. We also investigate some connections between $C$-Gorenstein projective, injective and flat modules of change of rings.},
author = {Yang, Xiao Yan, Liu, Zhong Kui},
journal = {Czechoslovak Mathematical Journal},
keywords = {$C$-Gorenstein projective module; $C$-Gorenstein injective module; $C$-Gorenstein flat module; -Gorenstein projective module; -Gorenstein injective module; -Gorenstein flat module},
language = {eng},
number = {4},
pages = {1109-1129},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$C$-Gorenstein projective, injective and flat modules},
url = {http://eudml.org/doc/196860},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Yang, Xiao Yan
AU - Liu, Zhong Kui
TI - $C$-Gorenstein projective, injective and flat modules
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 1109
EP - 1129
AB - By analogy with the projective, injective and flat modules, in this paper we study some properties of $C$-Gorenstein projective, injective and flat modules and discuss some connections between $C$-Gorenstein injective and $C$-Gorenstein flat modules. We also investigate some connections between $C$-Gorenstein projective, injective and flat modules of change of rings.
LA - eng
KW - $C$-Gorenstein projective module; $C$-Gorenstein injective module; $C$-Gorenstein flat module; -Gorenstein projective module; -Gorenstein injective module; -Gorenstein flat module
UR - http://eudml.org/doc/196860
ER -

References

top
  1. Christensen, L. W., Frankild, A., Holm, H., 10.1016/j.jalgebra.2005.12.007, J. Algebra 302 (2006), 231-279. (2006) Zbl1104.13008MR2236602DOI10.1016/j.jalgebra.2005.12.007
  2. Enochs, E. E., Jenda, O. M. G., Relative Homological Algebra, de Gruyter Exp. Math. Walter de Gruyter and Co., Berlin, (2000). (2000) MR1753146
  3. Enochs, E. E., Iacos, A., Jenda, O. M. G., 10.1215/ijm/1258138429, Illinois J. Math. 51 (2007), 561-569. (2007) MR2342674DOI10.1215/ijm/1258138429
  4. Holm, H., 10.1016/j.jpaa.2003.11.007, J. Pure Appl. Algebra 189 (2004), 167-193. (2004) Zbl1050.16003MR2038564DOI10.1016/j.jpaa.2003.11.007
  5. Holm, H., Jørgensen, P., Cohen-Macaulay homological dimensions, Rend. Semin. Mat. Univ. Padova 117 (2007), 87-112. (2007) MR2351787
  6. Holm, H., Jørgensen, P., 10.1016/j.jpaa.2005.07.010, J. Pure Appl. Algebra 205 (2006), 423-445. (2006) MR2203625DOI10.1016/j.jpaa.2005.07.010
  7. Holm, H., White, D., 10.1215/kjm/1250692289, J. Math. Kyoto Univ. 47 (2007), 781-808. (2007) Zbl1154.16007MR2413065DOI10.1215/kjm/1250692289
  8. Kasch, F., Modules and Rings, London Math. Soc. Monogr. Academic press, London (1981). (1981) Zbl0527.16001MR0667346
  9. Lam, T. Y., Lecture on Modules and Rings, Springer Verlag, New York (1999). (1999) MR1653294
  10. Yang, X., Liu, Z., 10.1017/S1446788709000093, J. Aust. Math. Soc 87 (2009), 395-407. (2009) MR2576573DOI10.1017/S1446788709000093
  11. Osborne, M. S., Basic Homological Algebra, Graduate Texts in Mathematics, Springer, New York, Berlin (2000). (2000) Zbl0948.18001MR1757274
  12. Park, S., Pusan, E. C., 10.1007/s10587-004-6409-5, Czech. Math. J. 54 (2004), 573-578. (2004) MR2086717DOI10.1007/s10587-004-6409-5
  13. Rotman, J. J., An Introductions to Homological Algebra, Academic Press, New York (1979). (1979) MR0538169
  14. Sazeedeh, R., 10.1016/j.jpaa.2004.01.010, J. Pure Appl. Algebra 192 (2004), 265-274. (2004) Zbl1087.13004MR2067199DOI10.1016/j.jpaa.2004.01.010
  15. Trlifaj, J., 10.1215/ijm/1258488170, Illinois J. Math. 47 (2003), 529-538. (2003) Zbl1035.16006MR2031338DOI10.1215/ijm/1258488170

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.