Geodesic
A Decomposition of Rings Generated by Faithful Cyclic Modules
Canadian mathematical bulletin, Tome 32 (1989) no. 3, pp. 333-339

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A ring R is said to be generated by faithful right cyclics (right finitely pseudo-Frobenius), denoted by GFC (FPF), if every faithful cyclic (finitely generated) right R-module generates the category of right R-modules. The class of right GFC rings includes right FPF rings, commutative rings (thus every ring has a GFC subring - its center), strongly regular rings, and continuous regular rings of bounded index. Our main results are: (1) a decomposition of a semi-prime quasi-Baer right GFC ring (e.g., a semiprime right FPF ring) is achieved by considering the set of nilpotent elements and the centrality of idempotnents; (2) a generalization of S. Page's decomposition theorem for a right FPF ring. 
Birkenmeier, Gary F. A Decomposition of Rings Generated by Faithful Cyclic Modules. Canadian mathematical bulletin, Tome 32 (1989) no. 3, pp. 333-339. doi: 10.4153/CMB-1989-048-9
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     author = {Birkenmeier, Gary F.},
     title = {A {Decomposition} of {Rings} {Generated} by {Faithful} {Cyclic} {Modules}},
     journal = {Canadian mathematical bulletin},
     pages = {333--339},
     year = {1989},
     volume = {32},
     number = {3},
     doi = {10.4153/CMB-1989-048-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-048-9/}
}
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