Quotient rings of rings generated by faithful cyclic modules

Birkenmeier, Gary F.

doi:10.1090/S0002-9939-1987-0883391-0

Quotient rings of rings generated by faithful cyclic modules
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Proc. Amer. Math. Soc. 100 (1987), 8-10 Request permission

Abstract:

A ring $R$ is said to be generated by faithful cyclics (right finitely pseudo-Frobenius), denoted by right GFC (FPF), if every faithful cyclic (finitely generated) right $R$-module generates the category of right $R$-modules. A fundamental result in FPF ring theory, due to S. Page, is that if $R$ is a right nonsingular right FPF ring, then ${Q_r}(R)$ is FPF. In this paper we generalize this result by providing a necessary and sufficient condition for a right nonsingular right GFC ring to have an FPF maximal right quotient ring.

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