Journal article
On two conjectures of Faith
Journal of algebra, Vol.367, pp.166-175
10/01/2012
DOI: 10.1016/j.jalgebra.2012.06.003
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.
Details
- Title: Subtitle
- On two conjectures of Faith
- Creators
- M Haim - Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, UruguayM.C Iovanov - University of Bucharest, Fac. Matematica & Informatica, Str. Academiei nr. 14, Bucharest 010014, RomaniaB Torrecillas - Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04071 Almería, Spain
- Resource Type
- Journal article
- Publication Details
- Journal of algebra, Vol.367, pp.166-175
- DOI
- 10.1016/j.jalgebra.2012.06.003
- ISSN
- 0021-8693
- eISSN
- 1090-266X
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 10/01/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985976502771
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