Identities on additive mappings in semiprime rings
Consider a ring $R$, which is semiprime and also having $k$-torsion freeness. If $F, d : R\to R$ are two additive maps fulfilling the algebraic identity $$F(x^{n+m})=F(x^m) x^n+ x^m d(x^n)$$ for each $x$ in $R.$ Then $F$ will be a generalized derivation having $d$ as an associated derivation on $R$....
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2023-01-01
|
| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/317 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1839636031062671360 |
|---|---|
| author | A. Z. Ansari N. Rehman |
| author_facet | A. Z. Ansari N. Rehman |
| author_sort | A. Z. Ansari |
| collection | DOAJ |
| description | Consider a ring $R$, which is semiprime and also having $k$-torsion freeness. If $F, d : R\to R$ are two additive maps fulfilling the algebraic identity $$F(x^{n+m})=F(x^m) x^n+ x^m d(x^n)$$ for each $x$ in $R.$ Then $F$ will be a generalized derivation having $d$ as an associated derivation on $R$. On the other hand, in this article, it is also derived that $f$ is a generalized left derivation having a linked left derivation $\delta$ on $R$ if they satisfy the algebraic identity $$f(x^{n+m})=x^n f(x^m)+ x^m \delta(x^n)$$ for each $x$ in $R$ and $k\in \{2, m, n, (n+m-1)!\}$ and at last an application on Banach algebra is presented. |
| format | Article |
| id | doaj-art-2ef15f76c5a848d6924d7e2c96dfea2a |
| institution | Matheson Library |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2023-01-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-2ef15f76c5a848d6924d7e2c96dfea2a2025-07-08T09:08:39ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202023-01-0158213314110.30970/ms.58.2.133-141317Identities on additive mappings in semiprime ringsA. Z. Ansari0N. Rehman1Department of Mathematics Faculty of Science Islamic University in Madinah, K.S.A Madinah, IndiaDepartment of Mathematics, Faculty of Science Aligarh Muslim University, Aligarh, IndiaConsider a ring $R$, which is semiprime and also having $k$-torsion freeness. If $F, d : R\to R$ are two additive maps fulfilling the algebraic identity $$F(x^{n+m})=F(x^m) x^n+ x^m d(x^n)$$ for each $x$ in $R.$ Then $F$ will be a generalized derivation having $d$ as an associated derivation on $R$. On the other hand, in this article, it is also derived that $f$ is a generalized left derivation having a linked left derivation $\delta$ on $R$ if they satisfy the algebraic identity $$f(x^{n+m})=x^n f(x^m)+ x^m \delta(x^n)$$ for each $x$ in $R$ and $k\in \{2, m, n, (n+m-1)!\}$ and at last an application on Banach algebra is presented.http://matstud.org.ua/ojs/index.php/matstud/article/view/317semiprime rings; generalized derivation; generalized left derivation and additive mappings |
| spellingShingle | A. Z. Ansari N. Rehman Identities on additive mappings in semiprime rings Математичні Студії semiprime rings; generalized derivation; generalized left derivation and additive mappings |
| title | Identities on additive mappings in semiprime rings |
| title_full | Identities on additive mappings in semiprime rings |
| title_fullStr | Identities on additive mappings in semiprime rings |
| title_full_unstemmed | Identities on additive mappings in semiprime rings |
| title_short | Identities on additive mappings in semiprime rings |
| title_sort | identities on additive mappings in semiprime rings |
| topic | semiprime rings; generalized derivation; generalized left derivation and additive mappings |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/317 |
| work_keys_str_mv | AT azansari identitiesonadditivemappingsinsemiprimerings AT nrehman identitiesonadditivemappingsinsemiprimerings |