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arXiv · 1110.2284

On two conjectures of Faith

M. Haim·M. C. Iovanov·B. Torrecillas
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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.

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M. Haim, M. C. Iovanov, B. Torrecillas. 2011-10-11. On two conjectures of Faith. https://arxiv.org/abs/1110.2284

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