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Keywords:
weak injective module; weak flat module; weak $n$-injective module; weak $n$-flat module; cotorsion theory
weak injective module; weak flat module; weak $n$-injective module; weak $n$-flat module; cotorsion theory
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
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