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 |
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Category: | math |
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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 |
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Date available: | 2022-08-22T08:26:36Z |
Last updated: | 2022-12-27 |
Stable URL: | http://hdl.handle.net/10338.dmlcz/150623 |
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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 |
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