Dissertation/Thesis Abstract

Baer and Rickart Properties in Modules and an Associated Radical
by LeBlanc, Richard L., Ph.D., University of Louisiana at Lafayette, 2014, 70; 3622944
Abstract (Summary)

In this work, module theoretic definitions of the Baer and related ring concepts are investigated. A module is s.Baer if the right annihilator of a nonempty subset of the module is generated by an idempotent in the ring. It is shown that s.Baer modules satisfy a number of closure properties. Under certain conditions, a torsion theory is established for the s.Baer modules, and examples of s.Baer torsion modules and modules with a nonzero s.Baer radical are provided. The other principal interest of this work is to provide explicit connections between s.Baer and projective modules. Among other results, it is shown that every s.Baer module is an essential extension of a projective module. Additionally, it is proven, with limited and natural assumptions, that in a generalized triangular matrix ring every s.Baer submodule of the ring is projective. Lastly, various definitions of Baer modules are considered and examples of modules satisfying multiple Baer properties are given. Numerous examples are provided to illustrate, motivate, and delimit the theory.

Indexing (document details)
Advisor: Birkenmeier, Gary F.
Commitee: Heatherly, Henry E., Magidin, Arturo, Ng, Ping Wong
School: University of Louisiana at Lafayette
Department: Sciences
School Location: United States -- Louisiana
Source: DAI-B 75/10(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Algebra, Baer rings, Modules, Nonsingular modules, Projective modules, Ring theory
Publication Number: 3622944
ISBN: 978-1-303-95115-2
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