A look at the faith conjecture

Translated title of the contribution: A look at the Faith Conjecture

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3 Citations (Scopus)

Abstract

A well known result of B. Osofsky asserts that if R is a left (or right) perfect, left and right selfinjective ring then R is quasi-Frobenius. It was subsequently conjectured by Carl Faith that every left (or right) perfect, left selfinjective ring is quasi-Frobenius. While several authors have proved the conjecture in the affirmative under some restricted chain conditions, the conjecture remains open even if R is a semiprimary, local, left selfinjective ring with J(R)3 = 0. In this paper we construct a local ring R with J(R)3 = 0 and characterize when R is artinian or selfinjective in terms of conditions on a bilinear mapping from a D-D-bimodule to D, where D is isomorphic to R/J(R). Our work shows that finding a counterexample to the Faith conjecture depends on the existence of a D-D-bimodule over a division ring D satisfying certain topological conditions. © Glasgow Mathematical Journal Trust 2000.
Translated title of the contributionA look at the Faith Conjecture
Original languageMultiple languages
Pages (from-to)391-404
JournalGlasgow Mathematical Journal
Volume42
Issue number3
DOIs
Publication statusPublished - 1 Sep 2000

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