Araştırma Makalesi
Yıl 2024,
Sayı: 47, 28 - 38, 30.06.2024
Öz
Let $\wp$ be a ring. It is shown that if an additive mapping $\vartheta$ is a zero-power valued on $\wp$, then $\alpha:\wp\rightarrow\wp$ such that $\alpha=\vartheta+1$ is a bijective mapping of $\wp.$ The main aim of this study is to prove that $\vartheta$ is a homoderivation of $\wp$ if and only if $\vartheta:\wp\rightarrow\wp$ such that $\vartheta=\alpha-1$ is a semi-derivation associated with $\alpha$, where $\alpha:\wp\rightarrow\wp$ is a homomorphism of $\wp.$ Moreover, if $\vartheta$ is a zero-power valued homoderivation on $\wp,$ then $\vartheta$ is a semi-derivation associated with $\alpha$, where $\alpha :\wp\rightarrow\wp$ is an automorphism of $\wp$ such that $\alpha=\vartheta+1$.
Anahtar Kelimeler
Kaynakça
- M. M. El Sofy Aly, Rings with some kinds of mappings, Master's Thesis Cairo University (2000) Cairo.
- J. C. Chang, On semi-derivations of prime rings, Chinese Journal of Mathematics 12 (4) (1984) 255-262.
- H. E. Bell, W. S. Martindale, Semiderivations and commutativity in prime rings, Canadian Mathematical Bulletin 31 (4) (1988) 500-508.
- M. Bresar, Semiderivations of prime rings, Proceedings of the American Mathematical Society 108 (4) (1990) 859-860.
- C. L. Chuang, On the structure of semiderivations in prime rings, Proceedings of the American Mathematical Society 108 (4) (1990) 867-869.
- E. Güven, Commutativity of semi-derivative prime rings, Indian Journal of Pure and Applied Mathematics 4 (2023) 1-8.
- E. Sögütcü, A characterization of semiprime rings with homoderivations, Journal of New Theory 42 (2023) 14 28.
- A. Melaibari, N. Muthana, A. El-Kenani, Centrally-extended homoderivations on rings}, Gulf Journal of Mathematics 4 (2) (2016) 62-70.
- A. Engin, N. Aydın, Homoderivations in prime rings, Journal of New Theory 43 (2023) 23-34.
- E. Güven, Homoderivations and their impact on Lie ideals in prime rings, Natural and Applied Sciences Journal 6 (2) (2023) 41-48.
- A. Sarikaya, Ö. Gölbaşı , Results on Lie ideals of prime rings with homoderivations, Extracta Mathematicae 38 (2) (2023) 125-137.
- I. N. Herstein, A note on derivations II, Canadian Mathematical Bulletin 22 (4) (1979) 509-511.
- J. Bergen, Derivations in prime rings, Canadian Mathematical Bulletin 26 (3) (1983) 267-270.
- E. C. Posner, Derivations in prime rings, American Mathematical Society 8 (6) (1957) 1093-1100.
Yıl 2024,
Sayı: 47, 28 - 38, 30.06.2024
Öz
Kaynakça
- M. M. El Sofy Aly, Rings with some kinds of mappings, Master's Thesis Cairo University (2000) Cairo.
- J. C. Chang, On semi-derivations of prime rings, Chinese Journal of Mathematics 12 (4) (1984) 255-262.
- H. E. Bell, W. S. Martindale, Semiderivations and commutativity in prime rings, Canadian Mathematical Bulletin 31 (4) (1988) 500-508.
- M. Bresar, Semiderivations of prime rings, Proceedings of the American Mathematical Society 108 (4) (1990) 859-860.
- C. L. Chuang, On the structure of semiderivations in prime rings, Proceedings of the American Mathematical Society 108 (4) (1990) 867-869.
- E. Güven, Commutativity of semi-derivative prime rings, Indian Journal of Pure and Applied Mathematics 4 (2023) 1-8.
- E. Sögütcü, A characterization of semiprime rings with homoderivations, Journal of New Theory 42 (2023) 14 28.
- A. Melaibari, N. Muthana, A. El-Kenani, Centrally-extended homoderivations on rings}, Gulf Journal of Mathematics 4 (2) (2016) 62-70.
- A. Engin, N. Aydın, Homoderivations in prime rings, Journal of New Theory 43 (2023) 23-34.
- E. Güven, Homoderivations and their impact on Lie ideals in prime rings, Natural and Applied Sciences Journal 6 (2) (2023) 41-48.
- A. Sarikaya, Ö. Gölbaşı , Results on Lie ideals of prime rings with homoderivations, Extracta Mathematicae 38 (2) (2023) 125-137.
- I. N. Herstein, A note on derivations II, Canadian Mathematical Bulletin 22 (4) (1979) 509-511.
- J. Bergen, Derivations in prime rings, Canadian Mathematical Bulletin 26 (3) (1983) 267-270.
- E. C. Posner, Derivations in prime rings, American Mathematical Society 8 (6) (1957) 1093-1100.
Toplam 14 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2024 |
| Gönderilme Tarihi | 12 Nisan 2024 |
| Kabul Tarihi | 26 Haziran 2024 |
| Yayımlandığı Sayı | Yıl 2024 Sayı: 47 |
Kaynak Göster
- Makale Dosyaları