Journal article
Module-theoretic generalization of commutative von Neumann regular rings
Communications in Algebra, Vol.47(11), pp.4713-4728
2019
DOI: 10.1080/00927872.2019.1593427
Abstract
Jayaram and Tekir defined an R-module M, R is a commutative ring, to be “von Neumann regular” if for each (Formula presented.) there exists an (Formula presented.) such that (Formula presented.) Previously, Fieldhouse called M “regular” if every submodule is pure and Ramamurthi and Rangaswamy called M “strongly regular” if every finitely generated submodule is a direct summand. We call these three notions JT-regular, F-regular, and strongly F-regular, respectively. We define M to be almost locally simple if for each maximal ideal (Formula presented.) of R, (Formula presented.) is either a trivial or simple (Formula presented.) -module and weakly JT-regular if (Formula presented.) for each (Formula presented.) We show that JT-regular (Formula presented.) almost locally simple (Formula presented.) strongly F-regular (Formula presented.) F-regular (Formula presented.) weakly JT-regular and investigate when these implications can be reversed. We provide some new characterizations of these properties and investigate each property in the context where M is finitely generated or R is Dedekind or more generally J-Noetherian. © 2019, © 2019 Taylor & Francis Group, LLC.
Details
- Title: Subtitle
- Module-theoretic generalization of commutative von Neumann regular rings
- Creators
- D.D. Anderson - University of IowaS. Chun - Chung-Ang UniversityJ.R. Juett - Texas State University
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.47(11), pp.4713-4728
- Publisher
- Taylor and Francis Inc.
- DOI
- 10.1080/00927872.2019.1593427
- ISSN
- 0092-7872
- Grant note
- DOI: 10.13039/501100003725, name: National Research Foundation of Korea, award: NRF-
- Language
- English
- Date published
- 2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984230628102771
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