Geodesic
Weak $n$-injective and weak $n$-fat modules
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 913-925
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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 \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
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
DOI : 10.21136/CMJ.2022.0225-21
Classification : 16D40, 16D50, 16E10, 16E30
Keywords: weak injective module; weak flat module; weak $n$-injective module; weak $n$-flat module; cotorsion theory 
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     journal = {Czechoslovak Mathematical Journal},
     pages = {913--925},
     year = {2022},
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Arunachalam, Umamaheswaran; Raja, Saravanan; Chelliah, Selvaraj; Annadevasahaya Mani, Joseph Kennedy. Weak $n$-injective and weak $n$-fat modules. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 913-925. doi: 10.21136/CMJ.2022.0225-21

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