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- W2000573036 abstract "We prove that a profinite algebra whose left (right) cyclic modules are torsionless is finite dimensional and QF. We give a relative version of the notion of left (right) PF ring for pseudocompact algebras and prove it is left–right symmetric and dual to the notion of quasi-co-Frobenius coalgebras. We also prove two ring theoretic conjectures of Faith, in the setting (and supplementary hypothesis) of profinite algebras: any profinite semiartinian selfinjective algebra is finite dimensional and QF, and any FGF profinite algebra is finite dimensional QF." @default.
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- W2000573036 date "2012-10-01" @default.
- W2000573036 modified "2023-09-28" @default.
- W2000573036 title "On two conjectures of Faith" @default.
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- W2000573036 doi "https://doi.org/10.1016/j.jalgebra.2012.06.003" @default.
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