Öz
Kaynakça
- 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.
Öz
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.
Anahtar Kelimeler
Prime ring semiprime ring source of primeness source of semiprimeness
Kaynakça
- 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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2022 |
| Gönderilme Tarihi | 15 Ekim 2022 |
| Yayımlandığı Sayı | Yıl 2022 Sayı: 41 |
Kaynak Göster
Cited By
The Source of $\Gamma$-Primeness on $\Gamma$-Rings
Mathematical Sciences and Applications E-Notes
https://doi.org/10.36753/mathenot.1389757
- Makale Dosyaları
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