Gorenstein Silting and FP-cosilting Modules

Abstract

In this paper, our goal is to introduce n-Gorenstein silting and n-(Gorenstein) FP-cosilting modules, and uncover the precise circumstances that are both required and sufficient for these modules to demonstrate the distinct features. We prove that the character module of an n-Gorenstein silting module with respect to finite-type

\mathbb{T}

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is n-Gorenstein cosilting. Furthermore, we give the connections between n-Gorenstein silting, n-Gorenstein tilting, n-Gorenstein star and n-Gorenstein quasi-tilting modules, and show that if a left R module T satisfies that Copres_G(Pres_Gⁿ(T)) = R-Mod, then the four above are equivalent, which more closely tie the silting, tilting and star theories in the context of Gorenstein homological algebras. We point out that the deleted n-Gorenstein projective (injective) resolutions of partial n-Gorenstein (co)silting modules are (n + 1)-Gorenstein pre(co)silting complexes. Finally, we introduce n-(Gorenstein) FP-cosilting modules. We investigate n-FP-cosilting over some extensions and obtain the relations among n-(Gorenstein) FP-cosilting, n-(Gorenstein) cosilting and Gorenstein weak n-silting modules.

Keywords

Gorenstein silting module / Gorenstein tilting module / Gorenstein star module / Gorenstein quasi-tilting module / Gorenstein FP-cosilting module / 18G25 / 16D40 / 16E05 / 16E30

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