When does an infinite ring have a finite compressed commuting graph?
In this paper, we show that any infinite ring has an infinite nonunital compressed commuting graph. We classify all infinite unital rings with finite unital compressed commuting graph, using semidirect product of rings as our main tool. As a consequence, we also classify infinite unital rings with only finitely many unital subrings.
Authors
- Nik Stopar (ORCID: https://orcid.org/0000-0002-0004-4957)
- Ivan-Vanja Boroja (ORCID: https://orcid.org/0000-0003-1836-0381)
- Damjana Kokol Bukovšek (ORCID: https://orcid.org/0000-0002-0098-6784)
Institutions
- University of Ljubljana (SI)
- University of Banja Luka (BA)
- Institute of Mathematics, Physics, and Mechanics (SI)
Publication Details
- Journal
- Journal of Algebra and Its Applications
- Published
- 2025-02-05
- DOI
- https://doi.org/10.1142/s0219498826501483
- Primary Topic
- Rings, Modules, and Algebras
- Type
- article
- Field-Weighted Citation Impact
- 0.00