Abstract
AbstractA 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.
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