Article
| 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: | [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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