A decomposition of rings generated by faithful cyclic modules

Gary F. Birkenmeier
1989 Canadian mathematical bulletin  
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 /^-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
more » ... er 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.
doi:10.4153/cmb-1989-048-9 fatcat:w23hr5lv2jcjhelqhtidufnxly