Geodesic
A Look at the FaithConjecture
Glasgow mathematical journal, Tome 42 (2000) no. 3, pp. 391-404

Voir la notice de l'article provenant de la source Cambridge University Press

A well known result of B. Osofsky assertsthat if R is a left (or right) perfect, left and right selfinjective ring thenR 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 theconjecture in the affirmative under some restricted chain conditions, the conjecture remains open evenif R is a semiprimary, local, left selfinjective ring withJ(R)^3=0. In this paper we construct a local ring R withJ(R)^3=0 and characterize when R is artinian or selfinjective interms of conditions on a bilinear mapping from a D-D-bimodule toD, where D is isomorphic to R/J(R). Our workshows that finding a counterexample to the Faith conjecture depends on the existence of aD-D-bimodule over a division ring Dsatisfying certain topological conditions. 
Ara, Pere; Nicholson, W.K.; Yousif, M. F. A Look at the FaithConjecture. Glasgow mathematical journal, Tome 42 (2000) no. 3, pp. 391-404. doi: 10.1017/S0017089500030081
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     title = {A {Look} at the {FaithConjecture}},
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     year = {2000},
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     doi = {10.1017/S0017089500030081},
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