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ANNIHILATORS AND A + B RINGS

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Date Issued:
2020
Abstract/Description:
A + B rings are constructed from a ring A and nonempty set of prime ideals of A. Initially, these rings were created to provide examples of reduced rings which satisfy certain annihilator conditions. We describe precisely when A + B rings have these properties, based on the ring A and set of prime ideals of A. We continue by giving necessary and su cient conditions for A + B rings to have various other properties. We also consider annihilators in the context of frames of ideals of reduced rings.
Title: ANNIHILATORS AND A + B RINGS.
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Name(s): Epstein, Alexandra Nicole, author
Klingler, Lee , Thesis advisor
Florida Atlantic University, Degree grantor
Department of Mathematical Sciences
Charles E. Schmidt College of Science
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2020
Date Issued: 2020
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 113 p.
Language(s): English
Abstract/Description: A + B rings are constructed from a ring A and nonempty set of prime ideals of A. Initially, these rings were created to provide examples of reduced rings which satisfy certain annihilator conditions. We describe precisely when A + B rings have these properties, based on the ring A and set of prime ideals of A. We continue by giving necessary and su cient conditions for A + B rings to have various other properties. We also consider annihilators in the context of frames of ideals of reduced rings.
Identifier: FA00013588 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2020.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Rings (Algebra)
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00013588
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.