Modules With Fi-Extending Hulls

Abstract

Abstract. It is shown that every finitely generated projective module P R over a semiprime ring R has the smallest FI-extending essential module extension H FI (P R ) (called the absolute FI-extending hull of P R ) in a fixed injective hull of P R . This module hull is explicitly described. It is proved that Q FI (End(P R )) ∼ = End(H FI (P R )), where Q FI (End(P R )) is the smallest right FI-extending right ring of quotients of End(P R ) (in a fixed maximal right ring of quotients of End(P R )). Moreover, we show that a finitely generated projective module P R over a semiprime ring R is FI-extending if and only if it is a quasi-Baer module and if and only if End(P R ) is a quasi-Baer ring.

Strongly Extending Modular Lattices

“…Another interesting related concepts of the extending modules is strongly FI-extending ( [13,15]). The strongly FI-extending property of modules has been used for the existence and description of the FI-extending module hull of any finitely generated projective module over a semiprime ring ( [14]). A module M is said to be a strongly FI-extending module if each fully invariant submodule is essentially contained in a fully invariant direct summand.…”

Baer module hulls of certain modules over a Dedekind domain

“…More recently, the notions of a Baer ring and a Rickart ring were extended to analogous module theoretic notions using the endomorphism ring S of the module by Rizvi, Roman, and Lee ([24] and [15] Recall from [4,Chapter 8] that the Baer ring hull of a ring R is the smallest Baer right essential overring of R in E(R R ). While some work has been done on the existence of a quasi-Baer ring hull of a ring R for some special classes of rings ([2], [3], and [4]), there is almost nothing known about the existence or description of Baer module hulls. To the best of our knowledge, the only explicit results about Baer ring hulls in existing literature have been due to Mewborn, Oshiro, and Hirano, Hongan and Ohori.…”