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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: 2024-10-04
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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