… module they called a ‘pure curve module in good position’. This paper generalizes their
construction by allowing more general modules… of the category of graded modules over a graded …

… to projective modules over integral domains R. We consider the case when the projective
modules … It is generally known that projective modules are direct sums of countably generated …

… In Section 3, we introduce and investigate dually Gorenstein weak projective modules in
terms of weak flat modules. In Section 4, we mainly investigate a class of relative right derived …

… 5 is an R-module decomposition. Since C is flat, e is a C-pure morphism; moreover, A = Ker(e)
… Hence, if C∗ ⇀ m is a C-pure R-submodule of M or C is a flat R-module, then the set C∗ ⇀ …

… of unital R-modules, the unadorned tensor product is understood to be over the ground
ring R. A submodule N of an R-module M is called W-pure, where W is an R-module, if the …

… All in all the approach chosen here leads to a clear refinement of the customary module
theory and, for M = Ä, we obtain well-known results for the entire module category over a ring …

… Firstly, it is clear from Lemma 3.1 that the class is extension closed and contains the projective
modules, as said modules are Cohen-Macaulay. If 0 → A → B → C → 0 is a short exact …

… In particular, any locally projective module is a flat module and is isomorphic with a …
projective modules are locally projective; moreover, there are described locally projective modules …

… ’s Lemma in Pure Projective Modules In the study of projective modules, we see a lemma
related to the equivalence of two modules N1 and N2, provided two projective modules P1 and …

… (Recall that a ring is said to be left-hereditary if all left ideals of the ring are projective
modules.) Fortunately, the condition satisfied by A implies that the corresponding bimodule is "…