C2-rings and the FGF-conjecture (Q2738761)

The C2-property was introduced by Utumi in his study of continuous rings, and a ring \(R\) is called a right C2-ring when every right ideal of \(R\) which is isomorphic to a direct summand of \(R_R\) is itself a direct summand. The authors make a survey of recent results on C2-rings, with special attention devoted to the impact of this condition on the FGF problem, which asks whether a ring for which every finitely generated right module embeds in a free module (called a right FGF-ring) is necessarily quasi-Frobenius. Among other results, they show that in order to give an affirmative answer to the FGF problem it is enough to prove that every right FGF-ring is a right C2-ring.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00043].