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- W1997011874 abstract "Let R be a ring and let simp- R be a representative set of all simple (right R -) modules. Denote by P < ω the class of all modules which are finitely generated and have finite projective dimension. The little finitistic dimension of R is defined by fdim( R ) = sup{proj.dim( M ) ∣ M ∈ P < ω }. Let ( A , B ) be the complete cotorsion theory cogenerated by P < ω . For each S ∈ simp- R , let f S : X S → S be a special A -precover of S . We prove that fdim ( R ) = max{proj.dim( X S ) ∣ S ∈ simp- R } provided that R is right artinian. As a corollary, we extend to right artinian rings the well-known Auslander–Reiten sufficient condition for finiteness of the little finitistic dimension." @default.
- W1997011874 created "2016-06-24" @default.
- W1997011874 creator A5084601516 @default.
- W1997011874 date "2001-12-01" @default.
- W1997011874 modified "2023-09-27" @default.
- W1997011874 title "Approximations and the Little Finitistic Dimension of Artinian Rings" @default.
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- W1997011874 doi "https://doi.org/10.1006/jabr.2001.8951" @default.
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