Balance functors and relative tilting modules (Journal Article)

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Abstract: Let \mathfrak {C} and \mathfrak {D} be two classes of left R-modules, l_{\mathfrak {D}}\mathfrak {C} = the class of all left R-modules admitting exact left \mathfrak {C}-resolutions which are \mathrm{Hom}(-,\mathfrak {D})-exact, r_{\mathfrak {C}}\mathfrak {D} = the class of all left R-modules admitting exact right \mathfrak {D}-resolutions which are \mathrm{Hom}(\mathfrak {C},-)-exact. We first study some properties of l_{\mathfrak {D}}\mathfrak {C} and r_{\mathfrak {C}}\mathfrak {D}. Then, using the Hom balance functor determined by the above two special classes of modules, we introduce and investigate F-(Wakamatsu) tilting and F-(Wakamatsu) cotilting modules which are possibly infinitely generated over arbitrary rings for an additive subfunctor F of \mathrm{Ext}^{1}(-,-). Some classical results are extended.