Abstract
There are three outstanding conjectures about quasi-Frobenius rings: The Faith conjecture that every left perfect, right selfinjective ring is quasi-Frobenius; The FGF-conjecture that every ring for which each finitely generated right module embeds in a free module is quasi-Frobenius; and The Faith-Menal conjecture that every right noetherian ring in which all right ideals are annihilators is quasi-Frobenius. In this paper we survey recent work on these conjectures and provide some new results on the subject.KeywordsDirect SummandLeft IdealFree ModuleNoetherian RingSemiprimary RingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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