Research Article
Year 2022,
Issue: 41, 100 - 104, 31.12.2022
Abstract
References
- N. Aydın, Ç. Demir, D. Karalarlıoğlu Camcı, The Source of Semiprimeness of Rings, Communications of the Korean Mathematical Society 33 (2018) 1083-1096.
- B. Albayrak, D. Yeşil, D. Karalarlıoğlu Camcı, The Source of Semiprimeness of Semigroups, Journal of Mathematics, 2021 (2021), Article ID 4659756, 8 pages.
- N. H. McCoy, The Theory of Rings, The Macmillan Company New York, Collier-Macmillan Ltd, London, 1964.
- T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Volume 131, Springer-Verlag, New York, 1991.
- T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, Springer-Verlag, New York, 1999.
- S. Ali, N. A. Dar, On Centralizers of Prime Rings with Involution, Bulletin of the Iranian Mathematical Society 41 (6) (2015) 1465-1475.
- H. Chimal-Dzul, S. Szabo, Classification of Nonsemicommutative Rings, Acta Mathematica Hungarica 165 (1) (2021) 48-62.
- A. Tarizadeh, M. Aghajani, On Purely Prime Ideals with Applications, Communications in Algebra 49 (2) (2021) 824-835.
Year 2022,
Issue: 41, 100 - 104, 31.12.2022
Abstract
In this study, we define a new concept, i.e., source of primeness of a ring $R$, as $P_{R} := \bigcap_{a\in R} S_{R}^{a}$ such that $S_{R}^{a}:=\{b\in R \mid aRb=(0)\}$. We then examine some basic properties of $P_{R}$ related to the ring’s idempotent elements, nilpotent elements, zero divisor elements, and identity elements. Finally, we discuss the need for further research.
References
- N. Aydın, Ç. Demir, D. Karalarlıoğlu Camcı, The Source of Semiprimeness of Rings, Communications of the Korean Mathematical Society 33 (2018) 1083-1096.
- B. Albayrak, D. Yeşil, D. Karalarlıoğlu Camcı, The Source of Semiprimeness of Semigroups, Journal of Mathematics, 2021 (2021), Article ID 4659756, 8 pages.
- N. H. McCoy, The Theory of Rings, The Macmillan Company New York, Collier-Macmillan Ltd, London, 1964.
- T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Volume 131, Springer-Verlag, New York, 1991.
- T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, Springer-Verlag, New York, 1999.
- S. Ali, N. A. Dar, On Centralizers of Prime Rings with Involution, Bulletin of the Iranian Mathematical Society 41 (6) (2015) 1465-1475.
- H. Chimal-Dzul, S. Szabo, Classification of Nonsemicommutative Rings, Acta Mathematica Hungarica 165 (1) (2021) 48-62.
- A. Tarizadeh, M. Aghajani, On Purely Prime Ideals with Applications, Communications in Algebra 49 (2) (2021) 824-835.
There are 8 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 31, 2022 |
| Submission Date | October 15, 2022 |
| Published in Issue | Year 2022 Issue: 41 |
Cite
Cited By
The Source of $\Gamma$-Primeness on $\Gamma$-Rings
Mathematical Sciences and Applications E-Notes
https://doi.org/10.36753/mathenot.1389757
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