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 Fully prime modules and fully semiprime modules Bull. Korean Math. Soc. 2020 Vol. 57, No. 5, 1177-1193 https://doi.org/10.4134/BKMS.b190864Published online September 30, 2020 John A. Beachy, Mauricio Medina-B\'arcenas Northern Illinois University; Av. San Claudio y 18 Sur, Col. San Manuel, Ciudad Universitaria, 72570 Abstract : Fully prime rings (in which every proper ideal is prime) have been studied by Blair and Tsutsui, and fully semiprime rings (in which every proper ideal is semiprime) have been studied by Courter. For a given module $M$, we introduce the notions of a fully prime module and a fully semiprime module, and extend certain results of Blair, Tsutsui, and Courter to the category subgenerated by $M$. We also consider the relationship between the conditions (1) $M$ is a fully prime (semiprime) module, and (2) the endomorphism ring of $M$ is a fully prime (semiprime) ring. Keywords : Prime submodule, fully prime module, semiprime submodule, fully semiprime module, regular module, fully idempotent module MSC numbers : Primary 16S90, 16N60, 16D60 Supported by : The research of the second author was supported by a Fulbright-Garc a Robles Scholarship while he was a Fulbright Scholar at Northern Illinois University Downloads: Full-text PDF   Full-text HTML