| Title:
|
Weak $n$-injective and weak $n$-fat modules (English) |
| Author:
|
Arunachalam, Umamaheswaran |
| Author:
|
Raja, Saravanan |
| Author:
|
Chelliah, Selvaraj |
| Author:
|
Annadevasahaya Mani, Joseph Kennedy |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
913-925 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 \hbox {$R$-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.\looseness +1 (English) |
| Keyword:
|
weak injective module |
| Keyword:
|
weak flat module |
| Keyword:
|
weak $n$-injective module |
| Keyword:
|
weak $n$-flat module |
| Keyword:
|
cotorsion theory |
| MSC:
|
16D40 |
| MSC:
|
16D50 |
| MSC:
|
16E10 |
| MSC:
|
16E30 |
| idZBL:
|
Zbl 07584108 |
| idMR:
|
MR4467948 |
| DOI:
|
10.21136/CMJ.2022.0225-21 |
| . |
| Date available:
|
2022-08-22T08:26:36Z |
| Last updated:
|
2024-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150623 |
| . |
| Reference:
|
[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 . |
| Reference:
|
[2] Chen, J., Ding, N.: On $n$-coherent rings.Commun. Algebra 24 (1996), 3211-3216 \99999DOI99999 10.1080/00927879608825742 . Zbl 0877.16010, MR 1402554 |
| Reference:
|
[3] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra.De Gruyter Expositions in Mathematics 30. Walter De Gruyter, Berlin (2000). Zbl 0952.13001, MR 1753146, 10.1515/9783110803662 |
| Reference:
|
[4] Gao, Z., Huang, Z.: Weak injective covers and dimension of modules.Acta Math. Hung. 147 (2015), 135-157 \99999DOI99999 10.1007/s10474-015-0540-7 . Zbl 1363.18011, MR 3391518 |
| Reference:
|
[5] Gao, Z., Wang, F.: All Gorenstein hereditary rings are coherent.J. Algebra Appl. 13 (2014), Article ID 1350140, 5 pages \99999DOI99999 10.1142/S0219498813501405 . Zbl 1300.13014, MR 3153875 |
| Reference:
|
[6] Gao, Z., Wang, F.: Weak injective and weak flat modules.Commun. Algebra 43 (2015), 3857-3868 \99999DOI99999 10.1080/00927872.2014.924128 . Zbl 1334.16008, MR 3360853 |
| Reference:
|
[7] Lee, S. B.: $n$-coherent rings.Commun. Algebra 30 (2002), 1119-1126 \99999DOI99999 10.1080/00927870209342374 . Zbl 1022.16001, MR 1892593 |
| Reference:
|
[8] Pérez, M. A.: Introduction to Abelian Model Structures and Gorenstein Homological Dimensions.Monographs and Research Notes in Mathematics. CRC Press, Boca Raton (2016). Zbl 1350.13003, MR 3588011, 10.1201/9781315370552 |
| Reference:
|
[9] Stenström, B.: Coherent rings and FP-injective modules.J. Lond. Math. Soc., II. Ser. 2 (1970), 323-329 \99999DOI99999 10.1112/jlms/s2-2.2.323 . Zbl 0194.06602, MR 258888 |
| Reference:
|
[10] Yang, X., Liu, Z.: $n$-flat and $n$-FP-injective modules.Czech. Math. J. 61 (2011), 359-369. Zbl 1249.13011, MR 2905409, 10.1007/s10587-011-0080-4 |
| . |
