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On radical ideals of non-commutative rings.
- Source :
- Journal of Algebra & Its Applications; Sep2023, Vol. 22 Issue 9, p1-17, 17p
- Publication Year :
- 2023
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- NONCOMMUTATIVE rings
JACOBSON radical
ALGEBRA
COMMUTATIVE rings
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 22
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 164930280
- Full Text :
- https://doi.org/10.1142/S0219498823501967