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Weak n -injective and weak n -fat modules

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 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...

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