Some results on G C -flat dimension of modules

Ramalingam Udhayakumar; Intan Muchtadi-Alamsyah; Chelliah Selvaraj

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 2, page 187-198
  • ISSN: 0010-2628

Abstract

top
In this paper, we study some properties of G C -flat R -modules, where C is a semidualizing module over a commutative ring R and we investigate the relation between the G C -yoke with the C -yoke of a module as well as the relation between the G C -flat resolution and the flat resolution of a module over G F -closed rings. We also obtain a criterion for computing the G C -flat dimension of modules.

How to cite

top

Udhayakumar, Ramalingam, Muchtadi-Alamsyah, Intan, and Selvaraj, Chelliah. "Some results on $G_C$-flat dimension of modules." Commentationes Mathematicae Universitatis Carolinae 60.2 (2019): 187-198. <http://eudml.org/doc/294818>.

@article{Udhayakumar2019,
abstract = {In this paper, we study some properties of $G_C$-flat $R$-modules, where $C$ is a semidualizing module over a commutative ring $R$ and we investigate the relation between the $G_C$-yoke with the $C$-yoke of a module as well as the relation between the $G_C$-flat resolution and the flat resolution of a module over $GF$-closed rings. We also obtain a criterion for computing the $G_C$-flat dimension of modules.},
author = {Udhayakumar, Ramalingam, Muchtadi-Alamsyah, Intan, Selvaraj, Chelliah},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$GF$-closed ring; $G_C$-flat module; $G_C$-flat dimension; semidualizing module},
language = {eng},
number = {2},
pages = {187-198},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some results on $G_C$-flat dimension of modules},
url = {http://eudml.org/doc/294818},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Udhayakumar, Ramalingam
AU - Muchtadi-Alamsyah, Intan
AU - Selvaraj, Chelliah
TI - Some results on $G_C$-flat dimension of modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 2
SP - 187
EP - 198
AB - In this paper, we study some properties of $G_C$-flat $R$-modules, where $C$ is a semidualizing module over a commutative ring $R$ and we investigate the relation between the $G_C$-yoke with the $C$-yoke of a module as well as the relation between the $G_C$-flat resolution and the flat resolution of a module over $GF$-closed rings. We also obtain a criterion for computing the $G_C$-flat dimension of modules.
LA - eng
KW - $GF$-closed ring; $G_C$-flat module; $G_C$-flat dimension; semidualizing module
UR - http://eudml.org/doc/294818
ER -

References

top
  1. Bennis D., 10.1080/00927870802271862, Comm. Algebra 37 (2009), no. 3, 855–868. MR2503181DOI10.1080/00927870802271862
  2. Christensen L. W., 10.1007/BFb0103984, Lecture Notes in Mathematics, 1747, Springer, Berlin, 2000. MR1799866DOI10.1007/BFb0103984
  3. Christensen L. W., Frankild A., Holm H., 10.1016/j.jalgebra.2005.12.007, J. Algebra 302 (2006), no. 1, 231–279. MR2236602DOI10.1016/j.jalgebra.2005.12.007
  4. Enochs E., Jenda O. M. G., Relative Homological Algebra, De Gruyter Expositions in Mathematics, 30, Walter de Gruyter, Berlin, 2000. Zbl0952.13001MR1753146
  5. Enochs E., Jenda O. M. G., Torrecillas B., Gorenstein flat modules, Nanjing Daxue Xuebao Shuxue Bannian Kan 10 (1993), no. 1, 1–9. MR1248299
  6. Foxby H.-B., 10.7146/math.scand.a-11434, Math. Scand. 31 (1972), 267–284. MR0327752DOI10.7146/math.scand.a-11434
  7. Golod E. S., G -dimension and generalized perfect ideals, Algebraic geometry and its applications, Trudy Mat. Inst. Steklov. 165 (1984), 62–66 (Russian). MR0752933
  8. Holm H., 10.1016/j.jpaa.2003.11.007, J. Pure Appl. Algebra 189 (2004), no. 1–3, 167–193. MR2038564DOI10.1016/j.jpaa.2003.11.007
  9. Holm H., Jørgensen P., 10.1016/j.jpaa.2005.07.010, J. Pure. Appl. Algebra 205 (2006), no. 2, 423–445. MR2203625DOI10.1016/j.jpaa.2005.07.010
  10. Holm H., White D., 10.1215/kjm/1250692289, J. Math. Kyoto Univ. 47 (2007), no. 4, 781–808. MR2413065DOI10.1215/kjm/1250692289
  11. Huang C., Huang Z., 10.1016/j.jalgebra.2010.10.010, J. Algebra 324 (2010), no. 12, 3408–3419. MR2735390DOI10.1016/j.jalgebra.2010.10.010
  12. Liu Z., Yang X., 10.1017/S1446788709000093, J. Aust. Math. Soc. 87 (2009), no. 3, 395–407. MR2576573DOI10.1017/S1446788709000093
  13. Rotman J. J., An Introduction to Homological Algebra, Pure and Applied Mathematics, 85, Academic Press, New York, 1979. Zbl1157.18001MR0538169
  14. Sather-Wagstaff S., Sharif T., White D., 10.1007/s10468-009-9195-9, Algebr. Represent. Theory 14 (2011), no. 3, 403–428. MR2785915DOI10.1007/s10468-009-9195-9
  15. Selvaraj C., Udhayakumar R., Umamaheswaran A., 10.1142/S179355711450051X, Asian-Eur. J. Math. 7 (2014), no. 3, 1450051, 13 pages. MR3257526DOI10.1142/S179355711450051X
  16. Vasconcelos W. V., Divisor Theory in Module Categories, North-Holland Mathematics Studies, 14, North-Holland Publishing Co., Amsterdam, American Elsevier Publishing Co., New York, 1974. MR0498530
  17. White D., 10.1216/JCA-2010-2-1-111, J. Commut. Algebra 2 (2010), no. 1, 111–137. MR2607104DOI10.1216/JCA-2010-2-1-111

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.