Fully prime modules and fully semiprime modules
Author ORCID Identifier
John Beachy: https://orcid.org/0000-0002-0338-1721
Bulletin of the Korean Mathematical Society
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.
Fully idempotent module, Fully prime module, Fully semiprime module, Prime submodule, Regular module, Semiprime submodule
Beachy, John A. and Medina-Bárcenas, Mauricio, "Fully prime modules and fully semiprime modules" (2020). NIU Bibliography. 117.
Department of Mathematical Sciences