Weak n -injective and weak n -fat modules

Umamaheswaran Arunachalam; Saravanan Raja; Selvaraj Chelliah; Joseph Kennedy Annadevasahaya Mani

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 3, page 913-925
  • ISSN: 0011-4642

Abstract

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We introduce and study the concepts of weak n -injective and weak n -flat modules in terms of super finitely presented modules whose projective dimension is at most n , which generalize the n -FP-injective and n -flat modules. We show that the class of all weak n -injective R -modules is injectively resolving, whereas that of weak n -flat right R -modules is projectively resolving and the class of weak n -injective (or weak n -flat) modules together with its left (or right) orthogonal class forms a hereditary (or perfect hereditary) cotorsion theory.

How to cite

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Arunachalam, Umamaheswaran, et al. "Weak $n$-injective and weak $n$-fat modules." Czechoslovak Mathematical Journal 72.3 (2022): 913-925. <http://eudml.org/doc/298438>.

@article{Arunachalam2022,
abstract = {We introduce and study the concepts of weak $n$-injective and weak $n$-flat modules in terms of super finitely presented modules whose projective dimension is at most $n$, which generalize the $n$-FP-injective and $n$-flat modules. We show that the class of all weak $n$-injective $R$-modules is injectively resolving, whereas that of weak $n$-flat right $R$-modules is projectively resolving and the class of weak $n$-injective (or weak $n$-flat) modules together with its left (or right) orthogonal class forms a hereditary (or perfect hereditary) cotorsion theory.},
author = {Arunachalam, Umamaheswaran, Raja, Saravanan, Chelliah, Selvaraj, Annadevasahaya Mani, Joseph Kennedy},
journal = {Czechoslovak Mathematical Journal},
keywords = {weak injective module; weak flat module; weak $n$-injective module; weak $n$-flat module; cotorsion theory},
language = {eng},
number = {3},
pages = {913-925},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak $n$-injective and weak $n$-fat modules},
url = {http://eudml.org/doc/298438},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Arunachalam, Umamaheswaran
AU - Raja, Saravanan
AU - Chelliah, Selvaraj
AU - Annadevasahaya Mani, Joseph Kennedy
TI - Weak $n$-injective and weak $n$-fat modules
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 3
SP - 913
EP - 925
AB - We introduce and study the concepts of weak $n$-injective and weak $n$-flat modules in terms of super finitely presented modules whose projective dimension is at most $n$, which generalize the $n$-FP-injective and $n$-flat modules. We show that the class of all weak $n$-injective $R$-modules is injectively resolving, whereas that of weak $n$-flat right $R$-modules is projectively resolving and the class of weak $n$-injective (or weak $n$-flat) modules together with its left (or right) orthogonal class forms a hereditary (or perfect hereditary) cotorsion theory.
LA - eng
KW - weak injective module; weak flat module; weak $n$-injective module; weak $n$-flat module; cotorsion theory
UR - http://eudml.org/doc/298438
ER -

References

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  1. Bravo, D., Gillespie, J., Hovey, M., The stable module category of a general ring, Available at https://arxiv.org/abs/1405.5768 (2014), 38 pages . (2014) 
  2. Chen, J., Ding, N., On n -coherent rings, Commun. Algebra 24 (1996), 3211-3216 9999DOI99999 10.1080/00927879608825742 . (1996) Zbl0877.16010MR1402554
  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. Gao, Z., Huang, Z., Weak injective covers and dimension of modules, Acta Math. Hung. 147 (2015), 135-157 9999DOI99999 10.1007/s10474-015-0540-7 . (2015) Zbl1363.18011MR3391518
  5. Gao, Z., Wang, F., All Gorenstein hereditary rings are coherent, J. Algebra Appl. 13 (2014), Article ID 1350140, 5 pages 9999DOI99999 10.1142/S0219498813501405 . (2014) Zbl1300.13014MR3153875
  6. Gao, Z., Wang, F., Weak injective and weak flat modules, Commun. Algebra 43 (2015), 3857-3868 9999DOI99999 10.1080/00927872.2014.924128 . (2015) Zbl1334.16008MR3360853
  7. Lee, S. B., n -coherent rings, Commun. Algebra 30 (2002), 1119-1126 9999DOI99999 10.1080/00927870209342374 . (2002) Zbl1022.16001MR1892593
  8. Pérez, M. A., 10.1201/9781315370552, Monographs and Research Notes in Mathematics. CRC Press, Boca Raton (2016). (2016) Zbl1350.13003MR3588011DOI10.1201/9781315370552
  9. Stenström, B., Coherent rings and FP-injective modules, J. Lond. Math. Soc., II. Ser. 2 (1970), 323-329 9999DOI99999 10.1112/jlms/s2-2.2.323 . (1970) Zbl0194.06602MR258888
  10. Yang, X., Liu, Z., 10.1007/s10587-011-0080-4, Czech. Math. J. 61 (2011), 359-369. (2011) Zbl1249.13011MR2905409DOI10.1007/s10587-011-0080-4

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