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- Title
On radical ideals of non-commutative rings.
- Authors
Groenewald, Nico
- Abstract
Let J (R) denote the Jacobson radical of a commutative ring R. In [H. A. Khashan and A. B. Bani-Ata, J -ideals of commutative rings, Int. Electron. J. Algebra 29 (2021) 148–164], the notion of J-ideals was introduced. If N (R) denotes the prime radical of a commutative ring then in [U. Tekir, S. Koc and K. H. Oral, n -Ideals of commutative rings, Filomat 31(10) (2017) 2933–2941], the notion of an N ideal of a commutative ring was introduced and studied. In this note, we show that these results are special cases of a more general situation. We define ρ -ideals for a special radical ρ and prove that most of the results of the above-mentioned papers are satisfied for non-commutative rings as a special case.
- Subjects
NONCOMMUTATIVE rings; JACOBSON radical; ALGEBRA; COMMUTATIVE rings
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 9, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823501967