Journal article
Atoms in quasilocal integral domains and Cohen-Kaplansky domains
Journal of Algebra and its Applications, Vol.20(6), 2150110
2021
DOI: 10.1142/S0219498821501103
Abstract
Let (R,M) be a quasilocal integral domain. We investigate the set of irreducible elements (atoms) of R. Special attention is given to the set of atoms in MM2 and to the existence of atoms in M2. While our main interest is in local Cohen-Kaplansky (CK) domains (atomic integral domains with only finitely many nonassociate atoms), we endeavor to obtain results in the greatest generality possible. In contradiction to a statement of Cohen and Kaplansky, we construct a local CK domain with precisely eight non-Associate atoms having an atom in M2. © 2021 World Scientific Publishing Company.
Details
- Title: Subtitle
- Atoms in quasilocal integral domains and Cohen-Kaplansky domains
- Creators
- D.D. Anderson - University of IowaK. Bombardier - University of Wisconsin–Platteville
- Resource Type
- Journal article
- Publication Details
- Journal of Algebra and its Applications, Vol.20(6), 2150110
- Publisher
- World Scientific
- DOI
- 10.1142/S0219498821501103
- ISSN
- 0219-4988
- Language
- English
- Date published
- 2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984230628202771
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