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• W4206147207 abstract "Let n be a positive integer, and let A be a strongly commutative differential graded (DG) algebra over a commutative ring R. Assume that (a) B=A[X_1,...,X_n] is a polynomial extension of A, where X_1,...,X_n are variables of positive degrees; or (b) A is a divided power DG R-algebra and B=A<X_1,...,X_n> is a free extension of A obtained by adjunction of variables X_1,...,X_n of positive degrees. In this paper, we study naive liftability of DG modules along the natural injection A-->B using the notions of diagonal ideals and homotopy limits. We prove that if N is a bounded below semifree DG B-module such that Ext_B^i(N, N)=0 for all i>0, then N is naively liftable to A. This implies that N is a direct summand of a DG B-module that is liftable to A. Also, the relation between naive liftability of DG modules and the Auslander-Reiten Conjecture has been described." @default.
• W4206147207 created "2022-01-26" @default.
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• W4206147207 date "2022-01-13" @default.
• W4206147207 modified "2023-09-29" @default.
• W4206147207 title "Naïve liftings of DG modules" @default.
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• W4206147207 doi "https://doi.org/10.1007/s00209-021-02951-z" @default.
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