Fully prime modules and fully semiprime modules

Author ORCID Identifier

John Beachy: https://orcid.org/0000-0002-0338-1721

Publication Title

Bulletin of the Korean Mathematical Society

ISSN

10158634

E-ISSN

22343016

Document Type

Article

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.

First Page

1177

Last Page

1193

Publication Date

9-30-2020

DOI

10.4134/BKMS.b190864

Keywords

Fully idempotent module, Fully prime module, Fully semiprime module, Prime submodule, Regular module, Semiprime submodule

Department

Department of Mathematical Sciences

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