ON FULLY BOUNDED NOETHERIAN MODULES AND THEIR ENDOMORPHISM RINGS

Nguyen Van Sanh; Oravan Arunphalungsanti; Nguyen Trong Bac; Sarapee Chairat

Nguyen Van Sanh
Oravan Arunphalungsanti
Nguyen Trong Bac
Sarapee Chairat

Keywords: bounded modules, fully bounded module, Jacobson’s conjecture

Abstract

In this paper we introduce the notion of bounded modules and fully bounded modules. A right R-module M is called a bounded module if every essential submodule of M contains a fully invariant submodule of M which is essential in MR. A module M is called a fully boundedmodule if M/X is bounded for any prime submodule X of M.