Balance functors and relative tilting modules

Lixin Mao ()
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Lixin Mao: Nanjing Institute of Technology

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 4, 1040-1055

Abstract: Abstract Let $$\mathfrak {C}$$ C and $$\mathfrak {D}$$ D be two classes of left R-modules, $$l_{\mathfrak {D}}\mathfrak {C}$$ l D C = the class of all left R-modules admitting exact left $$\mathfrak {C}$$ C -resolutions which are $$\mathrm{Hom}(-,\mathfrak {D})$$ Hom ( - , D ) -exact, $$r_{\mathfrak {C}}\mathfrak {D}$$ r C D = the class of all left R-modules admitting exact right $$\mathfrak {D}$$ D -resolutions which are $$\mathrm{Hom}(\mathfrak {C},-)$$ Hom ( C , - ) -exact. We first study some properties of $$l_{\mathfrak {D}}\mathfrak {C}$$ l D C and $$r_{\mathfrak {C}}\mathfrak {D}$$ r C 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 $$\mathrm{Ext}^{1}(-,-)$$ Ext 1 ( - , - ) . Some classical results are extended.

Keywords: Balance functor; F-Wakamatsu tilting module; F-Wakamatsu cotilting module; n-F-tilting module; n-F-cotilting module; 16D90; 16E05; 18G25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00320-y

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